This is a fragment of a startling drama, sadly not unique, in the life of a great scientist who dared to stand against the Atomists of this century. Atomism is a belief system which holds that by describing the particle composition of material an explanation is thereby produced not only of universal physicality but of all reality. It would reduce thought itself to contingent atomic reactions.

Duhem, not as a philosopher but as an physicist, confounded this Atomist cosmology at its very source by proving its incongruities and inconsistencies. As a result a blanket was thrown across his very name by those who have as their primary purpose personal glory and the hatred of anything that contradicts their philosophy of science; even when to do so they themselves have to distort even experimental facts. Such men ought never be accepted as scientists in the fullest meaning of that term — since they render all their findings doubtful by making them subject to personal opinions, ideologies and anti-intellectual bigotries rather than to testable reality. In the case of Duehm, they went further, conspiring to defraud a fellow scientist of his rightful recognition and rewards in this life. The foulest of these conspirators was Duhem's greatest and most implacable enemy, Berthelot, the man for whom a gold medal was cast boasting that while Paris faced death by starvation, he never missed a banquet at a restaurant frequented by his atheist peers.

Ironically, these proven obfuscators (and often liars) of whatever scientific discoveries stood against them are the very bigots who excised from our culture a millenium and more of scientific advance on the grounds that the dogmas of Christendom had polluted all human discovery until the Renaissance enthronement of humanist atheism.

This single chapter without entering upon that historical background I mention here, sets out the crisis of modern science as no other has done this century. Here Atomism meets the mystery of complexity (in a sense irreducible complexity), Newtonian energetics with Cartesian geometric explanations, intuitive genius with theoretical rigour — but always with an evil corroding thread interweaving the whole, human vainglory and lies.

After reading Uneasy Genius anger gives way to contempt, perhaps even sadness, for such wretched people as Berthelot and Lippman. Suddenly big names don't seem so big afterwards, even names like Paul Lengevin; and one is left wondering just how badly theoretical science, despite its explosion on the thrust of refined instrumentation, has been thwarted or even reversed. Dishonesty is not simply morally reprehensible; one must point out that it is also the greatest enemey of the human mind, and obviouslt inimical to science.

A more complete reading of Stanley Jaki's Uneasy Genius from which this excerpt is taken will also confirm what should have been obvious a generation ago concerning Berthelot whose name is still honoured; namely that he was a dishonourable and petty man who defended his position at any cost against modifications a\nd refutations imposed by Duhem who correctly investigated thermodynamic principles pertaining to maximum work theory. It will come as no surprise that the silencing of Duhem was undetaken by those who have subsequently led mankind into the simplistic quagmires of Scientism, where a blind faith in atomism as a unifying explanation of all reality now reigns supreme. Duhem dared to show that nothing was that simple. He also dared to imply that modern systems pretending to supply a philosophical coherence to such over-simplifications were at best irrelevant, at worst bunkum. But more, he dared to suggest that the mind, in being a repository of Common Sense, was best served by a philosophy which served that virtue without engaging the subject sciences directly, and indicated that we should re-examine the peripatetic methody, cleaned up of its ancient detritus and pagan theolog, which alone seems to allow the human intellect so to act.

Finally it should not be forgotten that Duhem stood, even when he was still unaware of the fact, against pagan Greece and ancient atomism, nothing less; nor should it be lost to us that had modern paganism not also swept away the philosophy that might have limited its wilder excess, such a fish-fowl of science and metaphysics, could never have developed such power to distort science in the first place.

For those who have picked up prejudices against the name of Pierre Duhem, the following must surely provide a timely caution …there are no doubt many paths we must retrace in order to correct our present follies at source. We could do worse than follow the thread back to Duhem and turn of the century France.
 
 

The making of a physicist

‘I have held it my duty as a scientist as well as my duty as a Christian never to cease being the apostle of common sense, the sole foundation of all scientific, philosophical, and religious certainty.’ So Duhem told a friend since youth in a letter of which four more phrases are known owing to the perspicacity of E. Picard, perpetual secretary of the Académie des Sciences, who made them the culminating point of his great eulogy of Duhem.¹ In the same letter Duhem met head on the classic objection to the central role of common sense. Were not its claims, he asked, ‘tantamount to some philosophical and religious beliefs, all resting on worthless reasonings which invariably imply undefinable notions, so many empty words void of meaning?’ As he tried to come up with an answer Duhem noticed that the same could be said in connection with all the sciences, including those which are considered the most rigorous among them’— physics, mechanics, and even geometry. The foundations of any of these constructs are formed by notions, which one pretends to understand although one cannot define them, or are formed by principles which one feels assured about, although one has no proof of them whatever. These notions, these principles are formed by common sense. Without this basis provided by common sense, a basis not at all scientific, no science can maintain itself; all of its solidity comes from there.
 
 

Such a declaration would more appropriately introduce a chapter on Duhem the philosopher, had Duhem not declared in the same letter that his philosophical work had the purpose of bearing out the ‘scientific truth’ of the primacy of common sense. To be sure, common sense was much more than mere consensus for Duhem, whose work as a physicist had dissent from consensus as a major characteristic. Lasting instructiveness is not, however, a necessary quality even of that dissent, such as Duhem’s, which is fully conscious and vastly articulated.
 
 

1. E. Picard, ‘La vie et l’oeuvre de Pierre Duhem’ (see note 53 to Ch. 7), pp. 40 41. The friend’s identity was not disclosed by Picard. The letter must have been written after 1906

because it contains a reference to La rhéorie physique.
 
 

That such a quality is part of Duhem’s dissent is better suggested by the fact that during his career as a physicist he had to dissociate himself, for one and the same reason, from two successive consensus. One was the consent which mechanistic physics was able to command, apparently in the name of common sense, even during its last two decades, the period coinciding with the first two decades of Duhem’s career. The other was the increasingly noticeable impact made during Duhem’s last ten years by relativity and atomic physics, both of which were markedly defiant of common sense in their origin and development.

To dissent from mechanistic physics in the name of common sense demanded much more than commonly attributed to it. That physical processes were so many impacts of moving bodies on one another seemed to be in full conformity with that common sense which merely demands that one may visualize what takes place. Descartes, who put so heavy a mark on French intellectuality, claimed common sense to his rationalism precisely because his physics could be readily imagined.²

Nor was Newton’s dissent from Cartesianism a serious threat to the role of imagination. While the Principia contained no references to mechanical models, the physical interactions dealt with there were not necessarily beyond the confines of common sense taken for visualizability. At any rate, the Queries of the Opticks were teeming with graphic descriptions of a wide variety of physical processes, including gravitation. This explains in part the fact that although the great tradition of French mathematical physics, from d’Alembert through Laplace to Fresnel, represented a shift of allegiance from Descartes to Newton, it never implied a strict disavowal of mechanical models. The warnings which Rankine, Kirchoff, and Mach gave in the 1870s about the fundamental weaknesses of mechanistic assumptions were not broadly appreciated prior to the turn of the century. The science of mechanics had by then become the ideal which other sciences were supposed to emulate.³ T. H. Huxley, who spoke of ‘trained and organized common sense’ as being science itself,⁴ was an advocate of a strictly mechanistic biology.

Duhem’s early and thorough exposure to the young science of thermodynamics did not trigger in him an immediate ‘break with mechanistic physics as an ideal. Whatever the non mechanistic framework in which thermodynamics, especially its second law, had originally been cast, by the 1880s there was emerging a mechanistic reinterpretation of it in terms of the kinetic theory of gases. Yet the fact that thermodynamics could deal with a vast range of phenomena without having recourse to assumptions about underlying mechanisms, was of no small significance. Duhem indeed attributed a crucial role in his formation as a physicist to two monographs he read, under Moutier’s guidance, during his last year at Stanislas, in both of which such assumptions were conspicuously absent.
 
 

2. And his mathematics too, as argued by P. Boutroux, L ‘imagination et les mathématiques se/on Descartes (Paris: Felix Alcan, 1900).

3. The extent to which this became true for biology and psychology is discussed in my The Relevance of Physics (Chicago: University of Chicago Press, 1966) ch. 7, and Brain, Mind and Computers (1969; South Bend, IN: Gateway, 1978), ch. 3.

4. ‘On the Educational Value of the Natural History Sciences,’ in T. H. Huxley, Science and Education. Essays (London: Macmillan, 1899), p. 45.
 
 

That the shorter of the two, Helmholtz’s memoir ‘Zur Thermodynamik chemischer Vorgange,’ was immediately brought to Duhem’s attention, tells as much of Moutier’s being abreast with the best in the latest as of his pupil’s capacity for it. Within twenty years the memoir became a small volume in Ostwald's Kiassiker der exakten Wissenschaften with a commentary by M. Planck who spoke of it as the ‘pioneering start of the development of pure thermodynamics, that is, the development of those theories of heat which disregard special kinetic hypotheses and confine themselves to the application of both of its two main laws.’⁵ The other and much larger monograph, Etudes sur les équi1ibres chimiques, was the work of Georges Lemoine, professor of chemistry at the Institut Catholique in Paris, who had just been called to a chair in the Ecole Polytechnique.

The monograph was part of an almost thousand page long volume, the second in a vast chemical encyclopedia published between 1882 and 1905 under the editorship of E. Frémy, but available as a separate volume already in 1881⁶ Moutier himself contributed to that second volume and so did Berthelot, who offered a 68 page long summary of the two volumes of his Essai de mdcanique chimique fondée sur la thermochimie.⁷ The chemical mechanics as set forth by Berthelot contained no assumptions about the mechanism of molecular interactions. He merely aimed at establishing the validity of the first law of thermodynamics in chemical processes measured on the macroscopic level. Such was an antimechanistic position insofar as it explicitly disregarded the question of the existence of atoms and of their machine like characteristics.

Not even that much was implied about mechanism in Moutier’s contribution on ‘some relations of physics and chemistry.’⁸ The physics Moutier had in mind was restricted to the two laws of thermodynamics. Lemoine’s large monograph, in which the question of underlying mechanisms was equally disregarded, came to a close with a summary of Gibbs’ theory of dissociation and with a report on Moutier’s finding the temperature independence of dissociation in gaseous systems.

There too references to mechanisms were absent.

Such were in their contexts the two works which, to quote Duhem’s words, ‘showed us the course which we have followed ever since never to depart from it.’ But this statement, the end of the first paragraph of the eighty printed pages in which in the spring of 1913 he summed up, at the request of the Académie des Sciences, his researches as a physicist,¹⁰ was preceded by a bow to Jules Moutier. The bow, conspicuous as it was, meant more than gratitude to a beloved teacher.
 
 

5. M. Planck (ed.), Hermann von Helmholtz. Abhandlungen zur Thermodynamik (Leipzig:

W. von Engelmann, 1902), p. 73.

6. G. Lemoine, Etudes sur les équilibres chimiques (Paris: Dunod, 1881), Tome I, Fasc. 2 in L’Encyclopédie chimique, dirigée par E. Frémy (Paris: Dunod, 1882 1905), pp. 69 380.

7. Ibid., pp. 1 68. The summary was, of course, that of the first edition (1979).

8. Ibid., pp. 387 431, followed by Moutier’s report on the allotropic transformation of phosphorus (pp. 437A G).

9. Ibid., pp. 361 67 and 36 7 78. Duhem, who by then more than suspected the slighting of Moutier by officialdom, must have been pleased by the recognition given by Lemoine to Moutier’s theoretical studies on dissociation (p. 367).

10. Notice sur. . . Pierre Duhem, 1913 (1), p. 36.
 
 
 
 

Duhem also wanted to remind the French scientific world of its rank failure to recognize and even to remember Moutier, by then long dead.¹¹ For as Duhem put it at the outset, Moutier, who made him love theoretical physics, not only initiated him into the applications of thermodynamics to chemical mechanics, a very new field in the late 1870s, but had to his credit the first of those applications to which he added several important ones.

In speaking of his own initiation Duhem must have had in mind his many private meetings with Moutier, because Moutier’s textbook of physics, which formed the basis of his instruction of students, who at Stanislas prepared for the Polytechnique or the Ecole Normale, did not contain, for all its vastness¹², more theory than could be carried by elementary calculus. Even Moutier’s Thermodynamique, a vast advance over his Eléments de thermodynamique, was no match in theoretical thrust to the two monographs mentioned above by Duhem. Only through private meetings with Moutier could young Duhem have been exposed to Moutier’s vast researches which were summarized by Moutier in a Notice, a booklet of 48 quarto pages published in 1881,¹⁵ when Duhem still had one more year to spend at Stanislas, not any more as a student but as an assistant teacher, In the Notice Moutier, then fifty one, gave a topical account of 138 published articles, notes, and memoirs under the following headings: heat, hydrostatics and capillarity, electricity and magnetism, acoustics, and optics. Of these headings, heat and electricity included the vast majority of Moutier’s researches. That this was to some extent true of Duhem’s researches as well, should indicate something of Moutier’s share in the making of Duhem the physicist. Duhem readily acknowledged that the orientation of his first tendencies was in the direction of Moutier’s own preferences,¹⁶ a fact strongly intimated by some of the subheadings under which Moutier grouped his publications on heat and electricity.¹⁷
 
 
 
 
 
 

11. Moutier must have died in 1897 or before, because his son, A. Moutier, a physician in Paris, thanked Duhem, in a letter of January 22, 1898, for a copy of Duhem’s ‘Thermochimie’ and above all for ‘what you have done there on behalf of my revered and beloved father.’ The reference was to the first volume of Duhem’s Traite élémentaire de mécanique chimique, 1897 (1), in which Moutier’s work is extolled on pp. 187 93. No biographical information on Moutier is available in the library and archives of the Ecole Polytechnique in spite of Moutier’s connections there as an alumnus and as a répétiteur.

12. J. Moutier, Cours de physique comprenant les matières d’enseignement de la classe des mathematiques spéciales (Paris: Dunod) of which the second volume (640 pp) dealing mostly with heat was published in 1884. The first volume (922 pp) dealt with hydrostatics, electricity, and optics, and appeared a year later. Both volumes first appeared in fascicules.

13. J. Moutier, La thermodynamique et ses principales applications (Paris: Gauthier Villars,

1885), 568 pp.

14. J. Moutier, Eléments de thermodynamique (Paris: Gauthier Villars, 1872), 163 pp.

15.Notice des travaux scientifiques de M. J. Moutier (Paris: Gauthier Villars, 1881). It is indicative of Moutier’s ability as a researcher that all those publications appeared within twelve years (1869 1881). According to the title page Moutier was inspector of the telegraphic services before he joined the faculties of the Polytechnique, Stanislas, and Ste Barbe.

16.Notice sur... Pierre Duhem, p. 36.
 
 
 
 

They also reveal Moutier’s close attachment to the work done in the chemical laboratories of the Ecole Normale since 1851 when Henri Sainte Claire Deville took there the chair of chemistry. The work largely centered on Deville’s finding in 1857, of the phenomenon he called dissociation.¹⁸ The finding, which showed that a limited and reversible chemical reaction could be produced by the mere application of heat, signalled the beginning of the field later called physical chemistry.¹⁹ Originally spoken of as chemical mechanics, the new field posed a major challenge to the principles of thermochemistry, a science initiated by the Danish chemist J. Thomsen and avidly cultivated in France by M. Berthelot.

Through Moutier young Duhem became familiar with the growing conflict between the chemists, such as Debray, Troost, and Hautefeuille, working at the Ecole under Deville’s leadership, and the ones grouping around Berthelot who kept adding political clout to his scientific renown. Since Moutier was heavily involved in the theoretical justification of the work done on dissociation, young Duhem could not help sensing that the sacred cause of truth was at stake, a cause which at the same time appeared patriotic as well. While the cause could freely advance abroad through the work of Gibbs, Maxwell, and Helmholtz, France seemed to be deprived of truth through Berthelot’s influence.²⁰ The prospect of helping to reverse that trend could but appeal to a young patriot like Duhem.

Moutier was not however a partisan spirit. Duhem imbued ample critical sense from Moutier, whom he described as ‘an ingenious theorist whose critical sense, ever alert and extremely perspicacious, distinguished with sure accuracy the weak point of many a system which others accepted without dispute.’²¹ Young Duhem certainly followed Moutier in the advocacy of mechanism, an advocacy all the more appealing as it was judicious:
 
 

Although Moutier appealed in his investigations to the most diverse methods, one after another it was to the mechanical attempts at explanation that he returned most often with a sort of predilection. Like most of the theorists of his time he saw the ideal of physics in an explanation of the material universe constructed in the manner of the atomists and the Cartesians. Being a disciple of Moutier, it was as a convinced partisan of mechanism that we approached the courses in physics taught at the Ecole Normale.²²
 
 

17. No less revealing are the titles of Moutier’s papers relating to hydrostatics and capillarity. The last of them, on the motion of bodies floating on the surface of liquids, is an application of Gauss’ theorem (see Notices des travaux scientifiques de M. J. Moutier, p. 30) which obviously influenced Duhem.

18. The subheading, ‘Applications a la chimie’ (ibid., pp. 23 26), begins with a reference to Sainte Claire Deville who is repeatedly mentioned thereafter.

19. As emphatically noted in the chapter, ‘Les sciences physiques et chimiques,’ by Brunhes, Duhem’s successor in Lille, in Un Siècle: Mouvement du monde de 1800 a 1900 (Paris: Librairie H. Oudin, 1900, p. 463), a topical evaluation of the 19th century, published by a committee under the presidency of Msgr. Péchenard. Its almost thirty contributors surveyed the 19th century under three headings: politico economical, intellectual, and religious.

20. That history is still to be written. There is not a hint of it in M. P. Crosland’s article, ‘Berthelot,’ Dictionary of Scientific Biography, 2:63 72.

21. ‘Physics of a Believer,’ in 1954 (3), p 275.

22. Ibid., p. 276.
 
 
 
 

Those courses and the courses in chemistry as well were taught in a decidedly anti mechanistic sense, that is, with a marked diffidence about hypotheses concerning the ultimate constitution of matter. Those who gave those courses were, in Duhem’s words, ‘past masters in experimental manipulation, they saw in experiment the only source of truth; when they accepted physical theory it was on condition that it rest entirely on laws drawn from observation.’²³

Such an acceptance of physical theory meant for all practical purposes little or no theory at all and invited a neglect of casting experimental results into an elaborate and rigorous mathematical framework. Herein lay an irony, unnoticed by Duhem, who described his teachers of physics and chemistry as ‘rivalling one another in praising the method that Newton had formulated at the end of his Principia.' 24 Whatever the true merits, unsuspected by Duhem, of Newton’s protestations against making hypotheses, Newton’s method certainly demanded a vast role for mathematics in physics. Those articulating that role were few and far between in France in the 1880s. Compared with the vigor which theoretical physics displayed in France during the first three decades of the century through the work of Laplace, Lagrange, and Fresnel, the situation during the following two generations represented a ‘certain fatigue.’ Blot, Arago, and Lame may have been the target of this remark with which Lucien Poincaré, a physicist by training and a high official in the French educational system, introduced his survey of French physics during the period

1870 1915. He understated the case. No less an understatement was his other remark that ‘one has to admit in all frankness that French physics ceased being the sole and the great initiator.’²⁵ France could boast around 1880 of only two major physicists, Fizeau and Regnault, both experimentalists. Mathieu, an outstanding theoretician, was languishing in the provinces. Henri Poincaré was still to give new luster to theoretical physics in France by extending the scope of his lectures at the Sorbonne where he arrived in 1881, at the age of twenty seven, with the reputation of a genius. As was already noted,²⁶ Duhem startled his fellow students specializing in mathematics at the Ecole Normale by his grasp of Poincaré's work. Poincaré was a great admirer of Hermite, who had already made a deep impression on Duhem the student at Stanislas.

Had young Duhem not been possessed by an unusual interest in physical theory insofar as it implied a heavy reliance on mathematics, he would not have found special stimulus in his teachers of mathematics at the Ecole, especially Jules Tannery. Thus, although theirs was the interest of pure mathematicians, they could but propel the development of a born theoretical physicist like Duhem as ‘they worked to develop and sharpen in us a critical sense and to make our reason infinitely difficult to satisfy when it had to judge the rigor of a demonstration.’²⁷
 
 

23. Ibid.

24. Ibid.

25. See Un demi siècle de civilisation francaise (1870 1915) by B. Baillaud and more than twenty other contributors (Paris: Hachette, 1916), p. 325.

26. See Ch. 2, pp. 43 4E

27.’Physics of a Believer,’ p276.
 
 
 
 

In fact an ‘ingenious theory of Moutier’ became one of the first victims of young Duhem’s quest for complete rigor.²⁸ The simultaneous impact on him of the teaching of single minded experimentalists and of no less single minded mathematicians was all that was needed in the way of external stimulus to carry toward completion the making of Duhem the physicist while still at the Ecole. This was true in a general as well as in a special sense, though not in that sense of unrestricted consistency which ultimately marked Duhem’s efforts as a theoretical physicist. Yet even in that latter respect the full formation of Duhem the physicist was not long in the making.

The general sense related to his viewing the ideal theory ‘as resting solidly on laws verified by experiment and completely exempt from hypotheses about the structure of matter . . . and at the same time . . . constructed with that logical rigor which the algebraists had taught us to admire.’ He was clearly in the grip of that view already in his last years at the Ecole. Otherwise he would not have stated that ‘we tried hard to make our lessons conform Ito that view] when we were given the first opportunity to teach’ in Lille.²⁹

Well before taking up his first teaching post there, Duhem had articulated that general idea in a specific sense. He seized in particular on the analogies between certain formulas of thermodynamics and mechanics. His reading of Gibbs, of Maxwell, and of Helmholtz acquainted him with the analogy between the notion of potential in mechanics and the function which Gibbs and Maxwell called ‘available energy’ and Helmholtz called ‘free energy’ in chemical reactions. ‘To treat the theories of thermodyamical statics by methods very similar in form to those in which, since Lagrange, mechanical statics is treated, such was the lasting concern of Gibbs and Helmholtz. The desire to set forth even more forcefully, if possible, the analogy guided our first researches.’³⁰ By these first researches Duhem obviously meant his rejected doctoral dissertation on thermodynamic potential and the papers leading to it.

Duhem’s years in Lille completed his making as a physicist in two respects. First, under the impact of the searching questions of his students — ‘an elite audience,’ to recall his glowing praise of them — he realized how difficult it was to live up with unrestricted consistency to the program of eliminating all mechanical hypotheses about the constitution of matter. Their ‘requests for clarification and embarrassing objections indefatigably indicated the paradoxes and vicious circles which kept reappearing despite our care ³¹ Revealingly, the most effective aspect of their quest for full clarity derived from their dissatisfaction with current treatises on thermodynamics. Little did Duhem suspect what was in store for him as he acceded to their request to put together a ‘small treatise on the foundations of that science’³² if it was to embody a complete absence of mechanistic assumptions, the invariable source of self defeating paradoxes and inconsistencies.
 
 

28. Introduction a la méchanique chimique, 1893 (1), pp. 159 61.

29. ‘Physics of a Believer,’ pp. 276 7.

30. Notice sur... Pierre Duhem, p. 37.

31. ‘Physics of a Believer,’ p. 277.

32. Not unexpectedly, the ‘small treatise’ grew into a vast memoir, the ‘Commentaire aux principes de la thermodynamique,’ 1892 (9), 1893 (11), and 1894 (2).
 
 
 
 

Complete success demanded nothing less than giving up the notion of physical method as an inductive procedure and as an explanation. Rather, physical theory, if fully conformed to logical rigor, was to become equivalent ‘to an artificial construction manufactured with the aid of mathematical magnitudes; … a kind of synoptic painting or schematic sketch suited to summarize and classify the laws of observation.’³³ Observations once stripped of any interpretative detail concerning the structure of matter, had to become statements about physical motion taken in the most general sense of any physical change. Herein lay the foundation of the kind of physics which Duhem later developed under the name of Energetics and which ultimately became the hallmark of his work in physics.

The second respect in which the making of Duhem the physicist was complete by the time he reached the mid point of his stay in Lille was the progress of his first researches which, as he stated, ‘very soon suggested to us a much broader idea.’³⁴ The latter consisted in a theory which may underlie two analogous domains, mechanical statics and physico chemical statics. To look for such a theory meant a procedure much more steeped in the exigencies of rigor than would have been the case with a mere attempt to reduce mechanics to thermodynamics. The theory in question implied a generalized notion applicable to any and all physical change. The main laws of that theory had therefore ‘to combine in a more conveniently generalized form the axioms of the old mechanics and the axioms of more recent thermodynamics.’ The prospects of the task beckoned to Duhem as a supreme challenge and a call. Or as he reminisced: ‘The formulation of such a science very soon appeared to us an objective so worthy that our life should be consecrated to its cultivation however imperfectly we may implement it’³⁵.

Whatever its breadth and depth, the validity of this notion of physics depended also on a sustained attention to the wide variety of experimental details . An early illustration of such attention was Duhem’s rejected doctoral dissertation which would have deserved acceptance even if it contained nothing else but that theoretical gem which later became a byword among physical chemists as the Gibbs Duhem equation. Long before Duhem reached this point in his Potentiel thermodynamique,³⁶ he had already offered a vast analysis of the ability of thermodynamic potential to account for the shape of curves established for vapour pressure in saline solutions. As to the equation in question, its formulation was preceded by a lengthy comparison of experimental data gathered during the previous two decades with two theories. One was Gibbs’ theory of dissociation in homogeneous and non homogeneous substances, the other was Helmholtz’s theory of heat produced in a voltaic pile. In fact, the equation, developed in the strictly theoretical chapter of the dissertation, served only to extend the range of experimental application of the thermodynamic potential.
 
 

33. ‘Physics of a Believer,’ p. 277.

34.Notice sur. . . Pierre Duhem, p. 37.

35. Ibid., p. 38.

36. Le potentiel thermodynamique, 1886 (I), p. 141, where its derivation is based on Euler’s theorem on homogeneous functions.
 
 
 
 

The extended range related to the problem presented by the combined etherification of more than two substances and to the problem of solubility of salt mixtures, e.xempt from double decomposition as well as subject to it. The heavy presence of experimental data in the third part of the dissertation was amply suggested by its caption: "Some applications of themodynamic potential to electrical phenomena.’³⁷ Not that all those data demanded the thermodynamic potential as a solution. In many cases, that is, in sufficiently energetic processes, its predictions were not significantly better than the ones provided by the maximum work principle. Yet, against such background one could sense all the more keenly the significance of a small group of data with which that principle could not cope.

Setting forth the theoretical significance of a novel approach in physics demanded then as now a mathematical articulation. The extent to which Duhem was able to do this already in his years of formation could be seen in his second or successful dissertation. In essence its subject was still the thermodynamic potential, although as related to magnetic induction.³⁸ This new viewpoint allowed for a heavy recourse to mathematical analysis which was also dictated by the practical consideration of making Duhem eligible to the only doctor’s degree still accessible to him, the degree in the mathematical sciences.

Duhem’s starting point was his conclusion at the end of a vast historical survey of the topic that the absence of complete rigor in Poisson’s mathematical treatment of magnetic induction had not been remedied by any subsequent study. He therefore derived the differential equation with partial derivatives which were required by the limiting conditions of the problem. He then showed that for magnetic bodies there existed one and only one solution for magnetization and that it corresponded to a state of stable equilibrium.

Concerning diamagnetic bodies Duhem’s mathematical analysis showed that if for such a body there existed a state of magnetic equilibrium, that is, a minimum of thermodynamic potential, then either that potential would present an infinity of other minima or there would exist a finite or an infinite number of unlimited and continuous series of magnetic distributions such that along each of them the potential in question always decreased. Paradoxical as such a result could appear, it provided a solution to some recent experiments.³⁹ Mathematical analysis led also to a conclusion opposite to a law stated by Faraday, a law which provided a distinction between magnetic and diamagnetic bodies. To provide a new basis for
 
 

37. Ibid., pp. 191 240.

38. 1888 (1).

39. It shows something of the paucity of experiments which Duhem’s physics called for that the experimental evidence he referred to was by 1913 a quarter of a century old. In fact, it was obtained during the very winter of 1887 88 when Duhem expected a decision on his second doctoral dissertation. Not that the evidence was not valuable. Paul Joubin, a year Duhem ‘s junior and a fellow Normalien, was a pr~parateur at the Coll’ege de France when he arrived at his results (‘Sur la mesure des champs magn~tiques par les corps magn~tiques,’ CR 106 [12 mars 18881: 735) without knowing of Duhem’s theory, a fact to which Duhem made a pointed reference in the printed form of his dissertation, 1888 (1), pp. 5 2 3. Duhem’s theory was not subjected to further tests by Joubin whose career eventually shifted to administrative posts.

268
 
 

their distinctness, Duhem had to make further mathematical recourse to the thermodynamic potential. For the case of two bodies, one very slightly magnetic, another very slightly diamagnetic, he could show that what was stable equilibrium for one, was unstable equilibrium for the other. While the answer was rigorous, it meant a drastic limitation of phenomena under consideration, a procedure also characteristic of the work of Duhem the physicist beyond his formative period. That in the same dissertation Duhem also considered the applicability of his main thesis to a broad variety of fields — thermic phenomena produced by magnetization, and to the behavior of crystallized bodies in magnetic fields — anticipated another feature of Duhem’s subsequent work in physics.
 
 

The physicist as seen by himself

Duhem saw his work in physics as an advance which had to be along a broad front with repeated returns to the same topics. The reason for this lay in the need to formulate theorems about the generalized notion of movement ajplicable to all branches of physics: ‘Only a large number of confrontations between those theorems and experimental physics could guarantee that the theory had acquired all the generality and precision desirable.’ Progress therefore meant ‘a series of tries and retouches’ and the realization that ‘it was necessary to be satisfied with sketches, gnesses, frequent reworkings and at the same time to forget about beautiful treatises setting forth the definitive truth in all its purity.’⁴⁰

While the ‘final word’ in physics was not the direct aim of that advance, it was to provide the basis of a consistent organization of all branches of physics, a precondition of approaching however remotely the definitive truth about the physical universe.

In 1913, when Duhem gave this characterization of his work as a physicist, he could look back on almost three decades of relentless research which certainly showed a unity of purpose and method. It was no exageration on his part to say that the only change in that research related to its label. What he first called ‘thermodynamique g~n~rale,’ or generalized thermodynamics, he later spoke of as ‘energ~tique.’⁴¹ Behind Duhem’s care to recall Rankine as the one who coined that word, there lay more than his bent on recognizing priority. Well before 1897, when Rankine was first recalled by Duhem in such a connection,⁴³ he must have seen the word in its German variant, Energetik, in the writings of Ostwald.⁴⁴ The latter’s grafting on the word a quasi metaphysical nuance could hardly endear it to Duhem whatever Ostwald’s interest in a generalized thermodynamics. Indeed, Duhem never dignified Ostwald’s ‘Energetik’ by so much as a mere reference. In Rankine’s use of the word Duhem could, however, find the intimation of a thermodynamics germane to his own approach to physical theory.⁴⁵ He could in fact show in his Notice with a long quotation from his commentaries on thermodynamics, published in the early 1890s, or years before he became familiar with Rankine’s paper, that he had by then a clear notion of thermodynamics as distinct from its mechanical interpretation and also from its definition as a strictly separate branch of physics.⁴⁶
 
 

40. Notice stir. Pierre Duhem, p.41.

41. See note 78 to Ch. 6.

42. Duhem, always quick to acknowledge priority and provenance, hardly knew of this before 1896.

43. Duhem did so in the preface to the first volume of his Traihi ~I~mentaire de m~canique chimique, 1897 (1), p. vi. Rankine first used the word energetics in his paper ‘Outline of the Science of Energetics’ (1885): see pp. 209 28 in his Miscellaneous Scientific Papers, ed. J. W. Millar (London: Charles Griffin, 1891).
 
 
 
 

Such a notion of thermodynamics did not have for its foundation, and not even for its starting point, hypotheses about the structure of matter, but abstract and formalistic axioms analogous to the ones on which Lagrange based his purely analytical mechanics.

The commentaries on thermodynamics were one of the five monumental studies representing the first phase in that advance along a broad front. The other four were studies relating to hydrodynamics, elasticity, chemical solutions, and electrodynamics, comprising in all half a dozen volumes, each covering almost 500 pages and published within four years (1891 94). The chief parts in the second phase were a four volume treatise on physical chemistry, and another series on hydrodynamical researches and elasticity. It was during that phase of about six years (1897 1903) that Duhem guided to successful conclusion half a dozen doctoral researches. The extensive analysis in them of experimental data was aimed at bringing further support to Duhem’s theoretical approach. The third phase (1910 1916) was largely represented by the two volumes of the Trait d’énergétique, a vast broadening of his commentaries on thermodynamics, and by a series of memoirs and notes on electrodynamics.
 
 

44. First in the article, ‘Studien zur Energetik,’ which Ostwald published in 1892 in his Zeitschrift fOr physikalische Chemie (9:563 78 and 10:363 86). Rankine was not mentioned either in this article or in the publications cited below. Three years later Ostwald regaled the French public with an article on energetics which in its German original had the revealing title, ‘Die Uberwindung des wissenschaftlichen Materialismus,’ a title toned down by the French editor to ‘La diroute de l’atomisme contemporain’ (RGScPA 6 [18951 :953 58). The same paper was read by Ostwald next year at the meeting of the German scientists in Lubeck. The subsequent major steps of the transformation by Ostwald of his Energetik into a monistic or panpsychistic Weltanschauung were his Vorlesungen fiber Naturphilosophie (1902), ‘The Modern Theory of Energetics’ (The Monist 17 [19071:481 515), and Der energetische Imperariv (191 2). The difference between Ostwald’s and Duhem’s notion of energetics is emphatically noted by R. Dugas in his posthumous work La th~orie physique au sens de Boltzmann et ses prolongements modernes (Neuchltel: Du Griffon, 1959), pp. 88 90.

45. As is very clear from Duhem’s discussion of Rankine’s ‘energetics’ in La th~orie physique. See its English translation, 1954 (3), pp. 52 53, where Duhem’s sole criticism concerns Rankine’s advocacy of the usefulness of starting with mechanistic hypothesis on the route toward a fully abstract theory.

46. Notice ...... Pierre Duhem, pp. 38 39. The quotation consisted of the concluding paragraph.
 
 
 
 

Since these three major phases were a variation on the same theme, Duhem could readily dispense with the historical perspective in summarizing his achievements as a physicist. His account, written mainly for the members of the Acad~mie des Sciences, was topical. More significantly, the account was interrupted only now and then by a brief mathematical formula and a very elementary one at that. This markedly non mathematical account could seem surprising in view of the heavy presence of mathematics in most of Duhem’s publications on theoretical physics. No less a mathematician than Hadamard spoke of Duhem’s Le~ons sur hydrodynamiquc as a source where he and other pure mathematicians had found powerful stimuli.⁴⁷ No wonder. According to Hadamard, Duhem was fully conversant, already when at the Ecole Normale, with the latest and best in mathematics offered by a Hermite and a Poincar~.⁴⁸

Complete mastery of all the mathematical tools helpful to the physicist was for Duhem a professional requirement to be taken for granted. It would have been inconceivable for him to rely on a hired mathematician as was the case with Einstein, who came to regret keenly his erstwhile neglect of mathematical studies. Duhem’s abstaining from mathematics in his Notice to the Acad~mie des Sciences was not primarily dictated by the practical consideration that many of its members would not have otherwise been able to peruse the eighty or so pages he devoted in that Notice to his work in physics. Far more decisive should seem in that respect Duhem’s notion of common sense as a foundation of physics.

It implied the translatability into ordinary language of physics, be it cast into the most esoteric mathematical moulds, The same translatability, it is well to recall, was upheld decades later by Einstein, Heisenberg, and Bohr,⁴⁹ who did so in connection with a physics far more removed from common sense than the physics done by Duhem. At any rate, his detailed account of himself as a physicist should seem to have interest of its own and all the more so because few if any other major physicists produced a similar document.

As could be expected from a thinker like Duhem, bent on rigor and logic, his first topic, or Section I of Part I of the Notice dealing with his work in physics, was the codification of the principles of energetics, Within the perspective of energetics motion in space (locomotion) could not be treated as a form of change simpler than any other change. All changes were on equal footing, they all were but modifications of systems. The notion of work too had to be much broader than the one issuing in locomotion. The concept of force, which in its Newtonian definition also related to spatial categories, namely, to the acceleration of moving bodies, had to yield to the concept of action. The notion of work thus broadened made possible a new definition of the quantity of heat, which in Duhem’s eyes was ‘one of the principal innovations’ of the doctrine of energetics.⁵⁰
 
 

47. 1. Hadamard, ‘L’oeuvre de Pierre Duhem dans son aspect mathimatique,’ in L’oeuvre scientifique de Pierre Duhem (Paris: A. Blanchard, 1928), p. 472. Hadamard mentioned

Volterra, and the Abb6 Coulon, a doctoral student around 1896 at the University of Bordeaux.

48. Ibid., p. 467.

49. According to Einstein, reliance on ‘the connection of the elementary concepts of everyday thinking with complexes of sense experiences . . . is the only thing which differentiates the great building which is science from a logical but empty scheme of concepts’ (Out of My Later Years [New York: Philosophical Library, 19501, p. 61). Heisenberg acknowledged that ‘even for the physicist the description in plain language will be a criterion of the degree of understanding that has been reached’ (Physics and Philosophy [New York: Harper Torchbook, 19621, p. 168). Heisenberg reported Bohr as having stated that ‘if we want to say anything at all about nature — and what else does science try to do? — we must somehow pass from mathematical to everyday language’ (Physics and Beyond [New York: Harper Torebbook, 19721, p. 135).
 
 

The new notion was to forestall any possibility, however subconscious, to define measurements of temperature in terms of hypotheses, however disguised, about the nature of heat.⁵¹

No such hypotheses seemed to be involved if the quantity of heat was defined so as to make the equivalence of heat and work its immediate consequence. This meant that classical mechanics, for which temperature changes were irrelevant, had to be viewed as a special or non normal case of energetics. The normal case was constituted by systems capable of temperature change, that is, having calorific capacity. The absorption of heat became thereby a mere rise in temperature which obtained its absolute scale through Carnot’s principle. While in statics the specification of temperature entailed no unusual consequences, the case was different for dynamics for the very reason that it could not be built as a mere amplication of d’Alembert’s principle, that is, as a generalization of the principle of virtual work of inertial actions, in addition, the principle of the virtual work of passive resistances or actions of viscosity had to be brought in because ‘those actions do not simply depend on the state of the system but also on its velocities [including] the velocities by which vary its most diverse properties, chemical, electrical, magnetic etc.’⁵²

A science of dynamics thus constituted had two limiting cases. One was Newtonian dynamics, corresponding to situations where viscosity played a negligible part. There acceleration was proportional to force. The other case was largely the realm of chemical reactions where the velocity of change was proportional to the action (or the product of force and time) producing it and therefore ‘reminds one of the old dynamics of Aristotle.’⁵³ One of the primary tasks of this new dynamics was the demonstration of the inequalities of Clausius, a particularly difficult task when parts of a system were at different temperatures.⁵⁴ Even more difficulties were presented by the isothermo isentropic systems as they could be treated only with the help of postulates extraneous to energetics. In singling out the problem of thermal conductivity in this connection, Duhem certainly showed keen awareness of the imperfections of his energetics. A chief of them was the constraint imposed on its cultivator to ignore deliberately areas of research teeming with unexpected advances and discoveries. In making this admission, both admirable and revealing, Duhem must have thought of radioactivity, spectroscopy, photoelectricity, and black body radiation. They all called for methods which assumed those very discontinuities that could not be considered in his energetics even as mere hypotheses.
 
 

50. Notice sur Pierre Duhem, p.4².

51. Duhem saw an evidence of the subtle presence of mechanical notions of heat in the endless efforts to submit measurements of heat to a great variety of corrections and asked: ‘Will these hypotheses become truly banished from science until there is on hand a notion of the quantity of heat, a definition so clear and general, that it implies no implicit and surreptitious appeal to assumptions which today are considered doubtful and even condemned?’ (ibid., p. 44).

52. Ibid., p. 46. All these velocities, Duhem added, ‘are marked by one characteristic: in any real modification the work effected by them is positive.’

53. Ibid., p. 47. This and other statements of Duhem about energetics as ‘analogous’ to Aristotelian dynamics became, as will be seen, so many pretexts in the hands of some for a

thorough misrepresentation of his thought as if he had advocated a return to Aristotle’s physics.
 
 

Energetics was also an imperfect science because of the magnitude of problems which in principle could be treated by it. A principal area of such problems was the mechanics of fluids and elastic bodies, a topic which took up almost one third (Sections II and Ill) of the summary of his work as a physicist and was a signal evidence of his courage to remain in the grip of most arduous problems. The unsatisfactory character of most propositions in Book II of the Principia, where Newton largely dealt with fluid mechanics, was symbolic of many subsequent efforts even with respect to the relatively simple case represented by homogenous and compressible fluids. Unlike in Newtonian mechanics, which made the interaction between two parts of such fluids a function of their masses, in generalized mechanics (a branch of energetics) the interaction became a function of their masses as well as of their densities.

Duhem’s first effort to make use of this idea in a memoir on the thermodynamic potential and hydrostatic pressure made him all too aware of ‘complications previously unsuspected.’ His subsequent efforts made him recognize that ‘while energetics brings new insights to hydrodynamics, they mostly make obvious the extreme difficulties of the theory.’⁵⁵

In his work on the mechanics of non viscous bodies Duhem made much of the supposition of ‘Very small motions’ though he did so with mixed feelings. He saw in it mere intuition which, however helpful, ‘deprived of the characteristic of infallible rigor all demonstrations which make use of it.’⁵⁶ The supposition made possible further studies of the stability of floating bodies in which he relied heavily on the criticism to which R. Clebsch, who ended his brief career as professor of mathematics in G6ttingen, subjected, around 1850, the metacenter rule, first proposed by Bouguer and later improved by Euler. Next came studies on floating bodies loaded with liquid because the ‘problem presented to energetics an opportunity to test its methods.’ If however, the problem was ‘not to remain a mere offshoot of the old mechanics, it had to be generalized,’ which in part was done through the introduction of the notion of associated displacement. Thus the difficulty which Clebsch pointed out with respect to the metacenter rule could be ,solved though only with a sixth degree equation, which showed that, when all its ots were positive, the equilibrium of a body oscillating on a compressible fluid was stable.⁵⁷
 
 
 
 

54. Ibid., p. 48. Here Duhem devoted much attention to the conductibility of heat and to the studies of Jouguet which ‘gave us an abundance of fruitful suggestions and profitable criticisms.’

55. Ibid., p. 52.

56. Ibid., p. 54.
 
 

While the complications of the hydrodynamics of non viscous fluids appeared frightening,’ those of viscous fluids seemed to Duhem ‘almost a cause for depair.’⁵⁸ He felt his work could alleviate but slightly the difficulties and described n detail only his work on the effects of viscosity within a fluid whose state hardly liffered from the critical state. The area of hydrodynamics where Duhem found matters relatively easy was the propagation of waves. Before him studies were restricted to the limiting cases of isothermic and adiabatic propagations. Since the intermediary cases remained unexplored, the method of energetics, Duhem remarked characteristically, ‘demanded that not the least lacuna be left in the series of cases to be explored.’⁵⁹ A particular area never studied before was the propagation of waves in viscous media. His principal finding was that in such media no waves could be propagated. Rigor therefore forced him to conclude that since air was a medium, however slightly viscous, sound waves were not real waves but quasi waves, that is, a sequence of very thin layers across which the partial derivatives of velocity varied rapidly though without discontinuity. In commenting on this he gave a revealing glimpse of the physics he was doing:
 
 

The study of the propagation of sound has so much imbued physicists with the notion of wave and its velocity of propagation that this kind of propagation appeared alone possible to them. They found it repugnant to admit that certain properties, such as temperature in a heat conducting medium, could exclusively depend on the analytic functions of the co ordinates [of space and of timel in such a way that in this kind of propagation there should be neither wave nor velocity. It is teasing to recognize that this is precisely the kind of propagation which applies to the motion of sound in air and that in the same case the existence of waves and the existence of a velocity of propagation are merely appearances and approximations.⁶⁰
 
 

Concerning the mechanics of elastic bodies Duhem found that the dynamics of such bodies presented far greater opportunities to him than their statics. The equations he obtained for the laws of viscosity within an elastic medium in motion allowed him the study of wave propagation in vitrous media with results analogous to the ones obtained for fluids. In a vitrous but non viscous medium with small deformations mathematical analysis predicted the separation of waves into a longitudinal and a transversal perturbation whose velocities were not the same. From the same equations, insofar as they governed the finite motions of elastic bodies, Duhem derived both rigorously and approximately valid propositions concerning states of equilibria. The subject matter demanded a sharp narrowing of the aspects under which it could be investigated, so that the results might be specific such as the inevitable instability of a medium in the case when an imaginary number represented the velocity with which an infinitely small perturbation moved within it.
 
 
 
 

57. Ibid., p. 56.

58. Ibid. ‘Allthose,’he quoted from his communication made in 1902(11) to the Acadimie, ‘who observed in a fluid the streaks and tracks which develop near the critical state, [and I who also observed the movements which are produced in the dissolution of hardly uniform concentrations, could note the extreme similarity of these two phenomena’ (ibid., p. 57).

59. Ibid., p. 58.

60. Ibid., p. 61.
 
 

The same subject allowed not only the refinement of previous studies but also the exploration of previously untouched fields. Among these was the motion of waves within elastic and viscous media affected by finite deformations. The impact of mathematical rigor was once more in full evidence as it predicted the breaking of waves in such media into eddies which, unlike ordinary eddies, could not slide past one another. Duhem’s work on such eddies (ondes cloison) was quickly verified by physicists, chemists, geologists, and astronomers. He viewed the outcome as a ‘valuable confirmation of one of the most general theorems formulated by mechanics based on energetics.’⁶¹

The method of energetics, a mathematical treatment of macrophysical transformations, however slight, of continua, was certainly germane to the theory of small movements of elastic bodies, a study initiated by Clebsch to whom Duhem often referred. For the same reason Duhem was attracted to Kirchoff’s theory of diffraction which in addition appeared to Duhem to be in need of a more rigorous formulation. The apparent disparity between the latter subject and the former posed no problem for energetics because its method barred concern about underlying mechanisms. On working with Clebsch’s theorem Duhem found close similarity among the statics of a flexible filament, the determination of the brachistochronous trajectory of a material point subject to a given potential function, and the route traced by a light ray in isotropic homogeneous media. ‘The analogies,’ wrote Duhem, ‘which are tied to this last problem, led us to discuss the stability of a flexible and inextensible fluid.’⁶²

An area most suited to the method of energetics was chemical mechanics (Section IV). In many works Duhem tried to organize fully the entire field by taking his lead from Gibbs’ memoir ‘On the Equilibrium of Heterogeneous Substances.’ In addition to rendering ‘irreproachable’ the formulation of the phase rule, Duhem also wanted to make it as general as possible through five propositions based on two postulates. One asserted the stable equilibrium of the homogeneous mixture of any number of fluids whose composition and temperature were variable, and which was under uniform and constant pressure. The other made the equilibrium of the mixture of any number of fluids the function of homogeneity, on the condition that the temperature and pressure remained the same. These postulates supported the general theorem: ‘If the temperature, pressure, and masses of independent components are given, and if these data are compatible with an equilibrium state of this system, the composition of each of those phases, within the system in equilibrium, is determined without any ambiguity.’⁶³ The consequence that no unstable chemical equilibrium was possible at a constant temperature, illustrated for Duhem a principal claim of energetics, namely, the absence of a rigid line of demarcation between physics and chemical mechanics.
 
 
 
 

61. Ibid., p. 67. Duhem was also pleased to note that the same kind of approach was used with respect to the mechanics of filaments and flexible membranes by L. Roy and Jouguet. Owing to their contributions, Duhem added, ‘this chapter of physical mechanics offers today a definitive, well rounded character.’

62. Ibid., p. 70.
 
 
 
 

The foregoing consequence concerning equilibria was found by Duhem particularly relevant for the study of mixed fluids, of their internal and external motions (Section V). He felt that unlike the kinetic theory of gases, which provided equations for particular cases, such as the diffusion of perfect gases into one another, ‘energetics provided a regular and general method for establishing the theory of motion of any number of mixed fluids.’ Generality meant no rigidity. In that sense Duhem could say that ‘energetics is not an exact science, jalthough] all theorems stated in it are subject to well defined conditions. Does a material system not fulfill one of these conditions? The correponding theorem must not then be applied.’⁶⁴ Such was Duhem’s introduction to his summary of his researches relating to friction and false equilibria (Section VI). Phenomena belonging under this head could not be handled by Carnot’s principle, a point acknowledged by Gibbs whom Duhem quoted at length.

Therefore, in Duhem’s view, there was a need of a ‘new energetics.’ ‘Old energetics’ (hardly two decades old yet) sufficed with a new chapter containing the doctrine of false equilibria, a doctrine which, as will be seen, did not elicit notable assent. Duhem’s study of a wave of first order with respect to the velocity with which chemical reaction propagates in a medium at the limit of false equilibrium was, however, recognized by some as a particular case of the propagation of an explosive impact or more generally of a shock wave. Duhem made particular mention of his work on the applicability of false equilibria to some electric phenomena. The reason for this was the affirmative answer which his last doctoral student obtained in 1908 to his suggestion made in 1896 that the decrease of electric charge brought about by exposure to ultraviolet light might be analogous to the decrease of viscosity under similar exposure.⁶⁵

The answer was both a registering of facts and their systematization in terms of energetics, which had to be stretched beyond its normal framework also in connection with some facts relating to permanent modification through magnetic hysteresis, the subject of Section VII of Duhem’s account of his physics. To cope with those facts, energetics had to be made more complete by adding one more variable to the equation governing thermodynamic equilibrium. One such fact closely investigated by Duhem, in part through the doctoral dissertation of Marchis, was represented by the behavior of what metallurgists called ‘hammered wire.’ Yet, a more ‘complete energetics’ could relieve a sense of chaos only to the extent of providing a ‘qualitative agreement’ between facts and theory.⁶⁶ By putting this admission in Italics Duhem served signal evidence how alien to him was any intention of concealing the shortcomings of his work.
 
 

63. Ibid., pp. 74 75.

64. Ibid., p. 78.

65. Ibid., p. 84. The author of the dissertation was Mine H. Baudeuf; see Cli. 6.

66. Ibid., p. 87.

276
 
 
 
 

Energetics could appear even more imperfect in respect to the magnetization of bodies (Section VIII). Imperfection meant that very often an extra term, which Duhem called electro kinetic energy, had to be added to the purely potential and kinetic energies which alone were assumed in ordinary energetics. The latter seemed to suffice in studying thermoelectric currents, a topic which early attracted Duhem’s attention. He was pleased to recall Poincarés qualification of his work as the one ‘which among all such works leaves the least to desire.’⁶⁷ Duhem also recalled his generalization of Lord Kelvin’s study of the problem known as w Mahomet’s coffin, that is, the question whether a piece of soft iron could be made to float in air by fashioning appropriately the magnetic field around it. The question was that of stable equilibrium and Duhem’s answer was, on the basis of energetics, negative.

Again, Duhem’s answer was negative with respect to the analogy often assumed between magnetized and dielectric bodies. He insisted that the distribution of electric and dielectric charge on a conducting body immersed in a dielectric medium implied a fictitious coefficient of polarisation in excess of the real coefficient. Maxwell’s use of one single rule in both cases prompted Duhem to considerable criticism. While algebraically rigorous, Maxwell’s procedure seemed to Duhem to do violence to the principles of mechanics and call ‘for the reconsideration of the problem by using in a possibly most exact manner the methods justified in energetics through the rigorous application of the principle of virtual displacements.’⁶⁸

The problem was also that of electrostatic pressure which Duhem investigated in detail. His solution, however praised, did not supplant ‘the paradoxical and indefensible theory of Maxwell,’ so Duhem mused by giving to Pascal’s dictum the variation: ‘Fashion has its reason which reason does not know.’⁶⁹ If failure to acknowledge priority was not so frequent in science as to constitute a fashion, it could happen time and again. An illustration of this was, according to Duhem, his account of pyro electric and piezo electric phenomena, and he quoted, somewhat philosophically, Lame: ‘Those who first pointed out these new procedures are no longer alive and will be wholly forgotten unless an archeologist mathematician will eventually revive their names.’ So be it, Duhem added, ‘what alone should matter is that science progressed.’⁷⁰ f

The longest of the Sections was the ninth and the last in which Duhem summed t up his extensive studies on electrodynamics and electromagnetism. He made it clear

from the outset that his originality did not consist primarily in tracing all electro c dynamics to virtual displacements. But unlike Helmholtz, who first noted this possibility and introduced electrodynamic energy as a postulate, Duhem called for t a full justification of it: ‘The mind has the right to request that it be not shocked by unexpected postulates as the laws of electrodynamics are successively obtained.’⁷¹ To satisfy this requirement Duhem took his starting point in E. Betti’s theorem on the connectivity of space.
 
 
 
 

67. Ibid., p. 88. On Poincar~’s remark see p. 280 below.

68. Ibid., p. 91.

69. Ibid., p. 92.

70. Ibid., p. 93. Lam6’s statement concluded his Le~ons stir les coordonn~es curvilignes et leurs diverses applications (Paris: Mallet Bachelier, 1859), p. 368.
 
 

A consequence of this procedure was a reinterpretation of the rotation of a magnet under the action of a current. What actually happened was rather to be seen as the impact exercised by currents and magnets on a mobile segment of a current which was linear. There followed the extension of the argument to conducting bodies of any dimension, by the dielectric or magnetic, where again Helmholtz was Duhem’s guide. One of his chief concerns was to determine the role of the constant, which Helmholtz denoted with K, in the case when magnetic and dielectric bodies were present. Equilibrium was assured when K was positive or zero. What would happen, Duhem asked, ‘if K was negative? Would it then be allowed to state that on an immobile conductor the electric equilibrium was unstable?’⁷³ On finding an answer, which appeared to him rigorous because of its purely algebraic structure, Duhem noticed its close similarity to the procedure he had used concerning the initial stability of an isotropic elastic medium. As could be expected, the fact that the same mathematical formalism covered two physical situations, which appeared drastically different to common sense, further confirmed Duhem in his conviction that the method of mathematical physics revealed nothing about the nature of reality.

While Duhem’s work in electromagnetics witnessed repeated reversals on particulars, such as the existence of diamagnetic bodies, the principal thrust of that work, a further articulation of Helmholtz’s theories, remained unchanged. Not only were those theories, in Duhem’s eyes, in agreement with all experimental data, but were also developed according to the dictates of the ‘most severe logic.’

Maxwell's electromagnetic theory, illogical in Duhem’s opinion on several accounts, became therefore the target of his relentless criticism. Duhem felt that only Helmholtz’s theory, which admitted not only transverse but also longitudinal flux, both in conducting bodies and in dielectric media, could rigorously account for the waves first detected by Hertz. The chief bone of contention was the so called displacement current which Maxwell postulated and which provoked the criticism of many prominent physicists, among them Poincaré, as being an ad hoc postulate and not a factor imposed by consistent logic. The explanation given by Maxwell’s supporters to Hertz’s experiments had to rest on the displacement current because the transverse flux had to be seen by them as localised largely in the region near the surface of a conductor placed in a field where the electric field oscillated in very short periods, In the theory given by Helmholtz, the longitudinal flux could function as the explanation, and all the more so as in Duhem’s belief the existence of that flux had received experimental confirmation through the experiments of Blondlot and also of Turpain, Duhem’s doctoral student Duhem recalled his criticism of Maxwell’s theory and turned it into the climax of his account of his own work in physics because he could thereby restate the ideal of physics he believed in.
 
 

71.Noticesur. .. Pierre Duhem,p. 94.

72. E. Betti (1823 1892) was professor of physics and mathematics at the University of Pisa since 1859. Duhem’s reference to Betti’s paper on spaces of any number of dimensions in Annali di matematica pure ed applicata (4 [18711:140 58) gives a glimpse of Duhem’s familiarity with Riemann’s work.

73. Notice sur. . Pierre Duhem, p. 97.

74. Ibid., p. 105.
 
 

According to Duhem the principal advantage of Helmholtz’s theory was its rigorously logical character. Quite different appeared to Duhem Maxwell’s work both in its genesis and development: ‘At the moment when logic suggested to Maxwell an order not to be transgressed, he overcame the inconveniencing obstacle by a flagrant default in reasoning or in calculus, convinced as he was that the target he wanted to reach was truth itself.’

That Maxwell was a genius was not questioned by Duhem: ‘The spectacle of those perilous jumps that led Maxwell to the target by defying rules, according to which the reasoning of ordinary humans is bound to proceed, reveals to our stupified admiration the very being of a genius.’ According to Duhem there were two ways of honoring such geniuses. One was a redoing of their work in terms ‘of the universal laws of logic,’ that is, ‘to trace out to the summit a safe route whose edges avoid the precipices which geniuses cross by a jump. Such was the way Helmholtz honored Maxwell. The other way was of those who believed themselves to have been better disciples of Maxwell by not looking into the meaning of his equations. Such disciples were Hertz, Cohn, Heaviside, and Boltzmann. Their attitude was expressed in Hertz’s famed dictum:

‘Maxwell’s theory is Maxwell’s system of equations.’⁷⁶ The defiance vis - vis difficulties, as expressed in that dictum, proved hollow, so Duhem argued, through the readiness of Hertz and Boltzmann to downplay the shortcomings in Maxwell’s reasonings. Maxwell’s theory had the even more serious difficulty of being in conflict with obvious facts. According to Duhem, Maxwell’s theory made impossible by defiAition the existence of such obvious bodies as magnets, because in that theory the magnetization of an isotropic body had to be a vector pointing in the same direction as the magnetic field.

The ultimate issue in physics was therefore a matter of attitude toward common sense evidence. Should a physicist start with facts provided by that evidence or by theories which, however successful, are burdened with an implicit denial of facts evidenced by common sense? Did not the slavish disciples of Maxwell act with respect to magnets, which they did not want to see, in much the same way as did Cremonini who declined to see the sunspots through the telescope so as not to jeopardize Aristotelian physics? Duhem’s own relentless logic could indeed prompt sweeping comparisons while it motivated unswerving dedication to a cause. His own relentless criticism of Maxwell’s theory was dictated. Duhem remarked, by the fact that ‘he did not want to renounce either the evidence of the senses or the laws of reason.’
 
 

75. Ibid.

76. By t913 this famous dictum of Hertz was over twenty years old. It first appeared in

Hertz’s introduction to his collection of papers on the detection of electromagnetic waves,

Untersuchungen Ober die Ausbreirung der elektrischen Kraft (1892); see English translation by

D. F. Jones, Electric Waves: Being Researches on the Propagation of Electric Action with Finite

Velocity through Space (1893;New York: Dover, 1962), p. 21.
 
 
 
 

Duhem’s consistent approach to problems of physics certainly supported his claim that all his intellectual career was meant to be an apostleship on behalf of common sense. That the case was more complex than seen by Duhem was unwittingly implied in his acknowledgment that his criticism of Maxwell prompted no major response. He felt victimized by disinterest in rigorous argumentation: ‘No reasoning can engage those unconcerned whether they are right or wrong.’⁷⁷ They were the physicists for whom it did not matter whether a theory was logical or absurd, and who asked of a theory only that, rightly or wrongly, it suggested new experiments.
 
 

Had this attitude become ‘general and final,’ Duhem would have had no choice but to consider his own life as a ‘signal waste.’ His confidence to the contrary was rooted in his trust in common sense claiming consistency. According to it, physical theory did not have for its unique role, not even for its principal role, the suggesting of new experiments. Its overriding role was ‘to classify and coordinate the chaos of facts revealed by experience.’ There was logic in this, and ‘since logic was eternal, it could be patient.’⁷⁸ Such was Duhem’s concluding remark on his work as a physicist. He felt no doubt that in the long run his work in physics would be given justice because of its logical consistency which, however, was above all residing mainly in its mathematical aspect. In 1913 Duhem was writing long memoirs devoted to the vindication of his electromagnetics.⁷⁹ As will be seen, within two years, and only one year before his death, he perceived a major logical fault in his work on electricity and magnetism. The outcome was not, as he seemed to believe, dictated by logic alone, but also by the evidence of senses, that is, facts, which ultimately prevail over logic, however rigorous. This turn came too late to be a part of the reaction by Duhem’s peers to his immense output in physics.
 
 

The physicist and his peers

‘Mr. Duhem combines two qualities which often exclude one another: a great erudition and a very systematic mind. These qualities, to which one should add a rare talent for presentation, are evident in all his publications which by now form a considerable amount.’ So Jules Tannery introduced his review, conspicuous by its length, of Duhem’s Hydrodynamique, Elasticité, Acoustique in the Bulletin des sciences matématiques. Thoroughly familiar with his former student’s way of thinking, Tannery gave an accurate portrait of what in terms of method the two large volumes meant to convey. Although mathematics was preponderant in both, they were ‘very much the work of a physicist who always has reality in mind,’ and, consequently, whose concern was not the complexity of mathematics but its ability to reveal about facts that unity which mere experience could not unfold:
 
 

77.Noticesur. . Pierre Duhem,p. 107.

78. Ibid.

79. See the memoirs 1913 (12), 1914 (6), and above all 1916 (11). The printing of the latter, submitted for the volume 1914 of AFScT was delayed by two years.
 
 

‘To draw all logical consequences from a very general principle, to show clearly what it contains and what it does not, and to specify the points where experiments must intervene to bring in something really new, such is the aim he pursues and undoubtedly he will thus contribute in a large measure to the organization of current science.’⁸⁰ By ‘current science,’ which Duhem aimed at organizing, Tannery may have meant not only an up to date hydrodynamics, viscosity, and acoustics but all branches of physics with their latest advances. If such was in 1893 Tannery’s notion, it would have anticipated, as will be seen, the central problem of Duhem’s work in physics.

For the time being the prospects for the organization of all ‘current science cotuld appear promising to a sympathetic reader of Duhem’s publications. One of them was Painlevd who contributed also in 1893 to the same Bulletin a dozen page long review of the three volumes of Duhem’s treatise on electricity. Painlev~, who like Tannery, wrote about Duhem on the basis of personal acquaintance and esteem, hcgan with a reference to the ‘innumerable treatises’ of very unequal merit which since Poisson had been written on electrical theory. To separate from that welter of material ‘the elements that had already become part of science and to fuse them into a single body of doctrine, is the daring enterprise which Duhem is not afraid to undertake.’⁸¹ Indeed, the appearance on the scene of a powerful systematizer was conjured up in Painlevd’s remark that the same thermodynamic potential, which in Duhem’s hands had already given a new unity to hydrodynamics, viscosity, vaporization, and dissociation, was now performing the same role with respect to electricity. Few physicists at that time, or at any other time, could expect the encomium which Duhem received from Painlevé: ‘The invariably analytical method adopted by Duhem gives to his book truly the character of power and unity.’⁸²

A signal recognition of Duhem’s excellence as a physicist came a year earlier from none other than Henri Poincaré. Only five years after he had approved Duhem’s doctoral dissertation, Poincaré made it clear enough that the former student was now his peer. The introduction of Poincarés lectures on thermo-dynamics came to a close with the paragraph: ‘Twice in the book I happened to be in disagreement with Mr. Duhem. He might wonder that I cite him only to combat him. I would be saddened if he thought of any ill will. I hope he will not suppose that I ignore the services he had rendered to science. I have only thought to be more useful by insisting on points where his results seemed to me to deserve complementing rather than on those points where I could but repeat him.’⁸³ The two points related to Duhem’s theory of dissociation and to his theory of the relation between the electromotive force at any given point and the heat developed there, and formed two sections in a book which Poincarés reputation carried far and wide. Poincaré submitted the second of those theories to a detailed and devastating criticism (‘Duhem’s theory becomes illusory’), because ‘it is the one which leaves the least to desire.’⁸⁴
 
 
 
 

80.BScMt7 (t893):22t 22.Thereviewwasof 1891 (2)

81. BScM 17 (t893):5. The review was of t891 (1) and 1892 (1).

82. Ibid., p. 15.

83. H. Poincar~, Thermodynamique. Le~ons profess&s pendant le premier semestre 1888

89, r~dig6es par J. Blondin (Paris: Georges Carr~, 1892), p. xix.
 
 

About the first theory Poincarés final dictum was ‘We can therefore admit Duhem’s hypothesis and accept Gibbs’ theory.’⁸⁵

Duhem’s reputation quickly spread across the Atlantic. W. D. Bancroft and E. Trevor, both professors at Cornell University, asked him to contribute to their newly founded Journal of Physical Chemistry. In its first volume Trevor introduced his review of Duhem’s Traité élémentaire de mécanique chimique ‘as one of the most notable publications of the year.’ Trevor found it difficult to ‘name anyone who is better qualified to give a connected and well rounded treatment of the subject than the famous theoretical physicist of the Bordeaux university.’⁸⁶

Six years later, in 1902, Duhem was spoken of in the same periodical as ‘the celebrated French physicist in a revsew of his Thermodynamique et chimie.⁸⁷ In the American Chemical Journal the same book was reviewed also in 1902 by Harry C. Jones, associate professor of chemistry at Johns Hopkins University, whose The Elements of Physical Chemistry was much in use during the first two decades of the century. Jones began his review with a reference to Duhem’s authority as ‘well recognized.’⁸⁸ Two years later the English translation of Duhem’s book was greeted by Jones as ‘a sign of the times and an indication of what the chemistry of the future will be.’⁸⁹

Such was a prophecy which Jones himself was not eager at all to implement. In the four revised and enlarged editions of his book, published between 1902 and 1915, Jones never referred to Duhem, an omission all the more ironic because in 1915 Jones saw the reason for the wide and constant demand for his book in a quality which after all was very Duhemian, namely, in its help ‘to transform chemistry from empiricism . . into science.’⁹⁰ Equally inconsistent with his enthusiasm for Duhem was Bancroft in his monograph on phase rule in which Duhem appeared only in a critical footnote.⁹¹ The American physicist who at that time truly lived up to his high regard for Duhem was E. Buckingham, professor of physics and physical chemistry at Bryn Mawr College. In his An Outline of the Theory of Thermodynamics Buckingham not only devoted a special chapter to Duhem’s theory of thermodynamic potential but also praised Duhem’s four volume treatise on chemical mechanics as a work ‘which makes a new volume of applications superfluous for the present.’⁹²
 
 
 
 

84. Ibid., p. 366

85. Ibid., p. 338.

86.JPhCH 1 (1896 97):427.

87. JPhCh 6 (t902):193. The reviewer was H. R. Carveth.

88. American Chemical Journal 28 (t902):242. Jones, however, took Duhem to task for

not recognizing the largely erroneous theoretical derivations which Henri Sainte Claire Deville

built upon his experiments.

89. American Chemical Journal 31 (t904):302.

90. H. C. Jones, The Elements of Physical Chemistry (4th revised ed.; New York: Macmillan,

1915), preface. Jones did not find it necessary to add Duhem’s name to those of L. Meyer, Ostwald, Nernst, and Van’t Hoff, whose great textbooks were listed in the preface to the first edition as his principal guides.

91. W. D. Bancroft, The Phase Rule (Ithaca N.Y.: The Journal of Physical Chemistry, 1897), p. 22. The criticism concerned Duhem’s putting in the class of ‘tabite equilibrium’ a mixture of hydrogen and oxygen.
 
 
 
 

The spreading of Duhem’s renown owed much to the attention given to his ptmblications in the Zcitschrift fur physikalische Chemie which Ostwald and Van’t Hoff launched in 1887. Soon the leading periodical in the field, the Zeitschrifr regularly carried reviews, most often by Ostwald himself, of Duhem’s books and major articles. Ostwald greeted the "Commentaires sur les principes de thermo-dynamique’ as a work whose sole defect was the absence in its title of the word ‘energetics’, which he had been advocating since l89l2. In 1896 Ostwald announced the reprinting of the Potentiel thermodynamique as a work which ‘played an important and influential role in the rapid development of the application of thermodynamics to the phenomena connected with physical and chemical equilibria.’

The book appeared to Ostwald as having by then a largely historical significance precisely because, as he put it, ‘the subject had meanwhile taken on a very different aspect in no small part through the indefatigable researches of the famed author.’⁹⁴ The appearance in 1899 of the fourth volume of the Mécanique chimique was described by Ostwald as ‘another monument to the famed author’s brilliant methods.⁹⁵

Naturally, Duhem was championed in Germany by G. F. Helm, professor of physics at the Technical Institute in Dresden, who unlike Ostwald did not fuse pseudo metaphysics into physics conceived as generalized thermodynamics or energetics. In a book on the mathematical principles of chemical change, which soon appeared in English translation as well, Helm spoke in 1894 of ‘the numerous and careful investigations of Duhem,’ which showed the usefulness of the thermodynamic potential for the mathematical treatment of chemical processes.⁹⁶ Three years later Helm described in his Energetik Duhem as ‘the first to recognize and thoroughly explore in an analytical perspective the great significance of Helmholtz’s method of using thermodynamics on the free energy function.’ Helm also gave proper credit to the Potentiel thermodynamique and to Duhem’s subsequent researches: ‘Since the publication of his book on thermodynamic potential this French investigator has reworked with rare incisiveness the entire field of theoretical science in order to subordinate it to this concept with ever increasing analytical rigor.’⁹⁷
 
 

92. E. Buckingham, An Outline of the Theory of Thermodynamics (New York: Macmillan, I 900), p. v. Of the twenty fivb principal books pertaining to the subject listed by Buckingham

tour were by Duhem.

93. ZPhCh 16 (1895):571. Ostwald’s ‘Studien zur Energetik’ (see note 44 above) was a rather elementary restatemens of the fact that energy was the common feature of all branches

of physics and no match either in extent or in depth to Duhem’s ‘Commentaires.’

94. ZPhCh 19 (t896):518.

95.ZPhCh 30 (t899):t83.

96. G. F. Helm, GrundzOge der mathematisehen Chemie: Energetik der chemischen Erscheioungen (Leipzig: Engelmann, 1894); see English translation by 1. Livingston R. Morgan, The Principles of Mathematical Chemistry: The Energetics of Chemical Phenomena (New York:

I. Wiley, 1897), p. 74. In the same context Helm declared that Berthelot’s principle of maximum work ‘has no theoretical foundation.’
 
 

Duhem must have been even more satisfied on seeing a few years earlier in Ladenburg’s massive dictionary of chemistry a long article by Planck who listed there four all important consequences drawn from the entropy function: two by Gibbs, one by Helmholtz, and one by him, namely, his thermodynamic potential as a magnitude that decreases in reactions taking place at constant temperature and pressure. Since many of the papers of L. Natanson, professor of physics in Cracow, were published in German, his sustained references to the importance of Duhem’s thermodynamics attested in a sense to his renown in German scientific ambience.

Quite different was the situation in France. Had Tannery not been co editor of the Bulletin des sciences mathématiques, Duhem’s books on hydrodynamics and electricity might not have been reviewed there. Such a guess is almost imposed by that general silence which greeted in France Duhem’s three volume Traité on electro-magnetic theory, a silence baffling in more than one sense.

After all, what Duhem implemented there in a systematic way was that critical attitude with which French physicists had already greeted Maxwell’s electromagnetic theory. The French translation of Maxwell’s classic work carried notes, more often critical than explanatory, by such leading French physicists as Cornu, Sarrau, and Potier.¹⁰⁰

The French reader was warned against "circularity in reasoning,’ against ‘definitions introduced in surreptitious ways which anyone not too familiar with the subject will but find absolutely arbitrary,’ against Maxwell’s mathematical use of the word induction which is ‘evidently inadequate and presented in an artificial manner,’ and against Maxwell’s ‘briskly passing from one concept of electricity to another.’ By the time the reader reached the second volume, where the sting of these remarks was dampened by a suggestion about their merely ‘didactic’ character, he must have already been negatively disposed also by the repeated references to the absence of empirical evidence on behalf of not a few of Maxwell’s inferences.
 
 
 
 

97. G. F. Helm, Die Energetik nach ihrer geschichtlichen Entwickelung (Leipzig: Verlag von Veit, 1898), p. 181.

98. M. Planek, ‘Thermochemie,’ in Handwdrterbuch der Chemie, edited by A. Ladenburg (Breslau: F. Trewendt, 1882 95), vol. XI (1893), pp. 566 646; on Duhem seep. 633. Planck’s article appeared also as a separate monograph under the title, Grundriss der aligemeinen Thermochemie (Brestau: F. Trewendt, t893); for reference to Duhem, see p. 117). Two years earlier, in a speech given at the meeting of Deutsche Naturforscher undArzte in tIalle, Duhem’s thermodynamic potential was listed by Planek as one of the important feats which assured the superiority of generalized thermodynamics (energetics) over kinetic theory. The text of Planek’s lecture, ‘Allgemeines zur ocueren Fntwicklung der Wtrmetheorie,’ was immediately printed in ZPhCh 8 (1891):647 56.

99. See, for instance, L. Natanson, ‘Ueber thermodynamisehe Potentiale,’ ZPhCh 10 (1892):

740; ‘Studien sur Theorie der Ldsungen,’ ZPhCh 10 (1892):748; ‘Ueber Zustandanderungen in einem von Bewegung begriffenen System,’ ZPhCh 26 (1898); 286, 289, 294 (an article which in a sense was a summary of Duhem’s work); and ‘Ueber die Fortpflanzung einer kleinen Bewegung in einer klelnen Fliissigkeit mit innerer Reibung,’ ZPhCh 40 (1902):584, 590.

100. J. Clerk Maxwell, Traiu~ de’e~lectricit~i et de magns~tisme, traduit de l’anglais sur la deuxi’eme hiition par G. Seligman Lul, avec notes et &laircissement par Cornu, Potier, et

Sarrau (Paris: Gauthier Villars et Fils, 1885 89), 2 vols.

101. Ibid., vol. 1, pp. 36, 53, 91, 106 and vol. 2, p. 148.
 
 
 
 

No small credit should have therefore been given to a work, like Duhem’s Traité, which carried rigor and completeness as its hallmark. At any rate, even on a mere inspection, Duhem’s work must have appeared superior to other major French monographs published previously on the subject in France by such notables as J.Bertrand¹⁰² and H. Poincaré, 103 both members of the Académie des Sciences.

Although Duhem’s Traité did impress Picard, he did not go public with his encomiums expressed in a letter to Duhem.¹⁰⁴ Somewhat understandable was the omission of Duhem in the second revised and enlarged edition of the lectures on electricity by Poincaré, an author never generous with references.¹⁰⁵ Such an excuse is not, however, applicable to E. Mascart who like Bertrand was professor at the Collège de France and published a much enlarged version, four years after Duhem’s Traité appeared, of his two volume textbook on electromagnetic theory.¹⁰⁶ The same may be said of the lectures which Brillouin gave on the propagation of electromagnetic effects in the Collège de France in l90l~02.107

If silence during the 1890s on Duhem in major French publications concerning electromagnetic theory was symptomatic, the silent treatment accorded to his work in thermodynamics makes it inevitable to assume that more than professional jealousy, unwilling to recognize the merit of potential competitors, was at play. The extra factor was academic politics, quietly orchestrated from behind the scenes.

This should seem obvious in view of what had been privately reported to Duhem about the intimidation which even some of his best and well positioned friends felt on the part of Berthelot. Absence of any reference to Duhem in the course given by H. Pellat on thermodynamics at the Sorbonne in 1985 96 could perhaps be excused by its elementary character.¹⁰⁸
 
 
 
 

102. J. Bertrand, Le~ons sur Ia rhhirie marh~matique de l’electricir~ (Paris: GauthierVillars, 1890). Bertrand claimed in the preface that it was legitimate to ignore, say, complicated multiple integrals, to which electrical theory led, whenever they did not appear to suggert experiments. Hardly a policy, Duhem might have said, appropriate to the highest level of scientific instruction in France.

103. H. Poincar~, Electricit~ et optique. I. Les th~ories de Maxwell et la th~orie ~lectromagnc~rique de Ia lumi~re. Le~ons professhis is Ia Sorbonne en 1888 89 et r6dig~es par J.

Blondin (Paris: Georges Carr~, 1890).

104. A letter quoted in Ch. 5.

105. H. Poincarti, Electricir~ er optique. La lumi~re et les rh~ories ~lectrodynamiques. Le~ons profess6es lila Sorbonne en 1888, 1890, et 1899. Deuxi~me edition, revue et compl6tl~e par J. Blondin et E. N&ulchs (Paris: Georges Carr~ et C. Naud, 1901).

106. Le~ons sur l’dectricit~ et Ic magn~tisme de E. Mascart et J. Joubert. Deuxi’eme hiltion entPerement refondue par F. Mascart (Paris: Masson, 1896 97). It must be noted that the two massive volumes of this work contained far more detailed information on experimental data and procedures than Duhem’s Traits. The first volume of the first edition was published in 1882 and served for young Duhem as introduction to the subiect. By 1886, when the second volume was published, Duhem’s grasp of electromagnetic theory was far superior to what was contained there.

107. M. Brillouin, Propagation de l’~lectricit~: Histoire et ths~orie (Paris: A. Hermann,

1904). Duhem’s omission in a book in which history and theory were treated together speaks

for itself.
 
 

No such explanation is possible a propos the introduction which Le Chatelier wrote to his translation of the first part of Gibbs’ memoir on the equilibria of homogeneous systems. Le Chatelier began with a reference to Sainte Claire Deville’s work on dissociation as the research which provided the most fertile terrain where Gibbs’ ideas could show their fruitfulness. Any fairly well informed reader could then expect a reference to Duhem, and all the more so because Le Chatelier was not forgetful of Duhem’s teacher, Moutier! Instead, Le Chatelier singled out, in 1899, a Schreinemakers, a Stortenbeker, a Mouret, and a Peslin — mostly unknown entities today even to a specialist historian — as chief implementers of Gibbs’ ideas, in addition to Roozeboom and Van’t Hoff,¹⁰⁹ as if Duhem himself had not written twelve years earlier the first critical study of Gibbs’ theories!

Possibly Le Chatelier, already a professor at the Collège de France, repaid some debt to Berthelot who indeed must have been grateful to Le Chatelier for his rear-guard defense of the maximum work principle.^1t0 This may also have been the case with Bernard Brunhes who in 1895, at twenty eight, obtained a chair of physics at the University of Dijon and in 1900 at the University of Clermont Ferrand where he also took the post of director of the Observatory of Puy de Dome. In an article, which he contributed to a book on the 19th century, Brunhes made much of the significance of thermodynamics in general and energetics in particular. He then deplored, though fleetingly, the fact that the new science of physical chemistry developed in the United States, Germany, and the Netherlands, while in France ‘an incorrect thermochemistry held all attention.’^11t

Of the role of Duhem in reversing that situation he could not be unaware, as he served two years in Lille as Duhem’s immediate successor. By the time Brunhes made up for his slighting of Duhem, a young physicist, H. Bouasse, to be known for the rest of his long life for his courage and outspokenness, broke the French silence on Duhem in a rather noteworthy context, the section on the history and philosopy of science in the International Congress for Philosophy held in Paris in 1900. There Bouasse brought his paper on the historical evolution of the principles of thermodynamics to a close with a glowing reference to ‘the admirable Traité de mécanique chimique by Duhem.’¹¹³
 
 
 
 

8. H. Pellat, Thermodynamique. Le~ons profess~es t~ la Sorbonne en 1895 96, r&lig~es par

Duperray & Goisot (Paris: G. Carve et C. Naud, 1897). The state of the art of teaching thermodynamics at the Sorbonne was welt attested by the reprinting, without any change, in 1905, of

Lippmann’s Thermodynamique (Paris: A. Hermann), which, already when first published in

1888, was distinctly inferior to Thermodynamique by J. Bertrand (Paris: Gauthier Villars,

1887).

109. J. W. Gibbs, Equilibre des syst~mes chimiques, tr. H. Le Chatelier (Paris: G. Carre & C. Naud, 1899); see especially pp. x xs.

110. A strange defense indeed! Le Chatelier ignored the theoretical falsity of the maximum work principle and denied that there had been any development from Mathieu’s characteristic functions to Duhem’s thermodynamic potential! See H. Le Chatelier, ‘Les principes fondamentaux de l’6nergetique et leur application aux phenom’enes chimiques,’ Journal de physique 3 (1894):289 306 and 352 71, especialiy p. 291, and also the summaries there (p. 381) of his communications to the Acad6mie des Sciences on that principle.

itt. B. Brunhes, ‘Les sciences physiques et chimiques,’ in Un si~cle: Mouvement du monde

de 1800 ~i 1900 (see note 19 above), pp. 440 70; for quotation, seep. 465.

112. Brunhes did so in his introduction to the translation by L. Roy of Gibbs’ memoir,

Diagrammes et surfaces thermodynamiques, a booklet (Nr 22) in the series Scientia (Paris:

Gauthier Villars, 1903), where he stated that Duhem with his work on thermodynamic

potential ‘brilliantly inaugurated a vast series of publications by which he made classic in

France the new thermodynamics’ (p. 7).
 
 
 
 

Such courage hardly appealed to those making up an academic establishment which Berthelot helped to shape to an oppressive extent. Henri Moissan, professor of chemistry at the Sorbonne, had already taken prominent part in the celebration of the 50th anniversary of Berthelot’s doctorate by setting forth his accomplishments in chemistry,¹¹⁴ before he was invited to the Congress on Sciences and the Arts at the St. Louis World Fair in 1904.

He was hardly the one to add Duhem’s name to those of Ostwald, Arrhenius, Gibbs, Van’t Hoff, Berthelot, and Thomsen as he surveyed the development of physical chemistry. French glory had to yield if Berthelot’s glory was at stake, the obvious reason why Duhem was asked to play but a secondary role in the International Congress of Physics in Paris in 1900, a role which he rightly declined in the name of French glory. Personal glory seems to have been at stake when in his two volume monograph on elasticity Brillouin found no room for a single mention of Duhem’s name.¹¹⁵

Duhem’s contribution to that field was much too well known to give Brillouin the possible excuse that his book was already in press when there appeared in 1906 in the Journal de chimie physiqtie the lines: ‘Duhem’s Recherches sur l’élasticité is an altogether original book in which the author gives for the first time the theory of elasticity in viscous media void of hysteresis. The book will retain all the more readily the attention of the scientific world because Duhem’s great competence to take up such a topic is well known. One cannot in fact find a more reliable guide to study the fundamental topics treated in that book. ¹¹⁶

A year earlier, in late 1905, there occurred possibly the most glaring instance of the silent treatment meted out to Duhem by a French physicist, since Berthelot avoided mentioning Duhem’s name in 1894 while trying to refute his criticism of the principle of maximum work.
 
 

113. H. Bouasse, ‘Sur l’histoire des principes de la thermodynamique,’ in Bibliotht~que du Congri’s International de Philosophie, III. Logique et Histoire des Sciences (Paris: Armand

Cohn, 1901), p. t3t.

114. H. Moissan, ‘Inorganic Chemistry: Its Relation with the other Sciences,’ in Congress of Arts and Sciences: Universal Exposition St Louis, 1904, vol. IV. Physics, Chemistry, Astronomy, Sciences of the Earth, edited by H. J. Rogers (Boston: Houghton, Mifflin, 1906), pp. 243

57.

115. M. Brillouin, Le~ons sur la viscositd des liqu ides et des gaz (Paris: Gauthier Villars,

1907). Brilouin’s lectures were, of course, based exclusively on the kinetic theory of gases.

116. JChPh 4 (t906)~576. The unsigned review was written most likely by the editor, Philippe A. Guye, professor of chemistry at the University of Geneva and safely outside of

Berthelot’s principate.
 
 

The occasion was the meeting of the Société francaise de philosophie on November 26, where Jean Perrin provided the subject of discussion with a paper on the essential contents of the principles of thermodynamics. Present at the meeting were such prominent figures as Brunschvicg, Delbos, Lachelier, Laberthonni&e, Le Roy, Li’vy Bruhl, Parodi, Painlevi’, Sorel, and Jules Tannery. At the outset Perrin contrasted atomism and energetics and specified the latter, which he equated with thermodynamics, as the sole subject of his presentation.

Actually, his chief concern was a vindication of atomism taken for a proof of materialism. The first half of Perrin’s lecture was reserved for the definition of the first and second laws which he gave so meticulously that those in the know, such as Painlevi’ and Tannery, could but think of Duhem, who was not mentioned by that very same Perrin who half a dozen years earlier had written to Duhem in order to learn from him, a principal authority in the field.

By 1905 Perrin felt no need for a contact with Duhem who could hardly be in sympathy with the thrust of Perrin’s lecture. At its midpoint Perrin turned to the question whether the second law, or the increase of entropy, was an absolute law or a mere statement of probability. Perrin was not, of course, the first advocate of a thoroughgoing materialism who tried to escape the vista of a cosmic end (and a cosmic beginning) which the law of entropy conjured up from the moment it was formulated by Clausius in 1873.

The inexorable decrease of available energy clearly rendered meaningless any adherence to the eternity of a matter forever active about which no less an antimetaphysician than E. Littri’ reminded in the the early 1 870s Frenchmen and others that it was the basic axiom of materialism.¹¹⁸ In fact, the second part of the discussion, which followed Perrin’s lecture, centered on that cosmological problem.

The first part of the discussion was largely a long restatement of the topic by Painlevé, who declared that Perrin provided ‘the best, if not the very best, presentation so far of the principles of energetics.¹¹⁹ If such was Painlevés way of reminding the audience of Duhem, it was a very covert way indeed. It may have given Duhem serious misgivings about Painlevé's trustworthiness as a friend, who as a member since 1900 of the Académie des Sciences, would have had nothing to fear had he not aspired to political glory as well. Whatever the merit of a very covert way of salvaging truth, it would have been called for also in connection with Perrin’s statement that the non atomistic interpretation of the second law had Lippmann for its chief spokesman in France! 120

While Perrin’s straight silence about Duhem could easily betray itself, recognition of Duhem could be given in such a way as to amount to rank slighting. A good example of this was provided by Perrin’s treatise on physical chemistry.^t21

Not only was it acknowledged there that Duhem gave the first rigorous definition of reversible transformations but also that he was correct to look at utilizable energy as a thermodynamic potential.¹²² Yet no sooner had Perrin stated that Duhem was right in claiming that the thermodynamic potential at constant pressure and volume provided a rigorous definition for stability, he continued with an encomium on the practical criterium of stability, which he identified of all things as the maximum work principle, stated by Thomsen and ‘independently formulated by Berthelot in 1864.’ The rest of the paragraph was a classic in talking away the issue and truth as well, and treating its sole and courageous champion as a nonentity:
 
 
 
 

117. The text of Perrin’s presentation and of the discussion are given in full in Bulletin de Ia Soci~rs~ fran~aise de philosophie 6 (1906): 81 lit.

118. E. Littri’, La science au point de vue philosophique (Paris: Didier, 1873), p. 322. A successor of Comte as unofficial pontiff of the positivist church, Littri’ added condescendingly

that ‘there was a time when one believed in the creation and destruction of substances.’

119. Bulletin de las SociLit~ fran~aise de philosophie 6 (1906): 105.

120. Ibid., p. 96.

121. J. Perrin, Traiti’ de chimie physique. Les principes (Paris: Gauthier Villars, 1903).
 
 
 
 

But the statement, rather obscure and too general, which Berthelot proposed, soon gave rise to violent polemics, and had to be restricted and specified. According to the ideas, which Berthelot himself reached in the end, the law of maximum work does not pretend any longer to dominate the entire physical chemistry. It leads to consequences which, though never exact, are all the less certain the higher is the temperature. However, the principle remains valuable, and I repeat, it forms actually the only practical criterium of stability.¹²³

Perrin, who after graduating from the Ecole Normale in 1893 was only offered a post in a lycée which he had refused, was still a mere chargé de cours, though at the Collage de France, under the tutelage of Brillouin. For his own advancement in Paris he had to bend truth, theoretical and historical, in favor of Berthelot. Part of the policy was to leave Duhem unmentioned at the crucial juncture. Not surprisingly, in the preface of his book Perrin attacked energetics together with its ‘theological obscurities,’¹²⁴ without making clear that he did not mean to implicate Duhem, the chief advocate of energetics in France, whose writings on the subject, unlike those of Ostwald, remained strictly scientific.

Not that Perrin, whose confidence in the victory of atomism could not have been greater, had been overly concerned about energetics. Duhem and his energetics left just as unimpressed other French physicists who at that time championed the cause of atomism. At most they dignified Duhem by voicing their disagreement with him. When Duhem wanted to obtain Brillouin as member of the jury examining Marchis’ thesis, Brillouin finally refused by stating that in his view all of Marchis’ experiments were a waste of time.¹²⁵
 
 

122. Ibid., pp. 135 and 197. Yet Perrin did not mention Duhem at all in the long chapter, ‘Le potentiel chimique’ (pp. 228 64)!

123. Ibid., p. 198. Naturally, Duhem was ignored in the works of other spirited defenders of the maximum work principle, such as Les th~ories physico chimiques (2d ed.; Paris: A. Hermann, 1901) by A. Reychler, professor at the University of Bruxelles, and Introduction Li l’~rude de thermodynamique (2d ed.; Paris: Gauthier Villars 1909) by R. Blondlot, professor at the University of Nancy.

124. Perrin, Traits de chimie physique, p. xiii.

125. ‘C’est un travail considi’rable et qu’il me serait agri’able de louer, sue ne trouvais qu’ll pi’che par Ia base m~me, et si je n’i’tais convaincu que tout ce soin, toutes ces heures et annLies de travall sont comme nuls et non avenus, et que de tout cela II ne restera rien’ (letter to Duhem, Febr. 22, 1898).
 
 
 
 

About the same time Brillouin expressed agreement only in a letter to Duhem with the scientific truth of the latter’s criticism of Berthelot.¹²⁶ In early January 1902, in thanking Duhem for a copy of his book on Maxwell’s electromagnetic theories, Pierre Curie made it clear that whatever the shortcomings of Maxwell’s theory, he did not find useful Duhem’s warnings against it. ‘I think it would be a good idea that our physicists display in Maxwell’s style an unheard imprudence, the very thing Duhem decried. ‘By what to replace Maxwell’s way of reasoning?’ asked Curie, who voiced his repugnance ‘to go back to purely mathematical formulas which represented nothing physically.’ After listing several disagreements between Maxwell’s theory and experiment, Curie told Duhem: ‘I am in complete disagreement with you concerning magnetism.’¹²⁷ And so was, of course, in physical chemistry, Le Chatelier, whose antagonism toward Duhem’s work lingered on for long among his disciples.¹²⁸

The only French physicist to take issue openly with Duhem was Paul Langevin, who did so in a speech delivered on February 18, 1904, at a symposium on the teaching of physics and mathematics held at the Musée de pédagogie.¹²⁹ A brilliant graduate of the Ecole Normale and a fellow in J. J. Thomson’s laboratory at Cambridge, Langevin was, with Perrin, a protégé of Brillouin, before Mascart asked him in 1902 to give a course at the Collége de France where he took Mascart’s chair in 1909. Whatever his fascination with the various new advances of corpuscular physics, Langevin, as will be seen shortly, did not remain even within one single speech consistent with his advice for keeping a balance between a mechanistic and a non mechanistic (thermodynamical) approach in physical method. Balance was indeed rudely upset when in praising the thermodynamical approach Langevin had place for Duhem only as the representative of an ‘energetics’ hardly different from that pseudo religion into which Ostwald had transformed it. It was a rude misstatement on Langevin’s part that Duhem simply advocated a return to Aristotelian physics of qualities, as if Duhem had not made it all too clear that his energetics included only such qualities that could be handled quantitatively.
 
 

126. Letter of Nov 29, 1897, in which Brillouin declared himself a ‘defender of Berthelot’ on the ground that he was always on the side of those ‘violently attacked.’ Brillouin sensed

nothing of the violence of the quiet attack with which Berthelot kept scuttling Duhem’s career.

127. This letter has been published by P. Brouzeng in his ‘Magni’tisme et i’nergi’tique. La mi’thode de Duhem. A propos d’une lettre ini’dite de Pierre Curie,’ Revue d’histoire des sciences

31 (1978):333 44.

t28. In acknowledging the receipt of a complimentary copy of Duhem’s Thermodynamique et chimie, Le Chatelier politely made it clear that he considered the book worthless (letter of March 9, 1902). As to the attitude of Le Chatelier’s students, the letter which R. Piontelli, professor of physical chemistry at the Politeenico of Milan, wrote to D. G. Miller on Jan 25, 1962, is bluntly revealing: ‘As far as Duhem’s enemies are concerned, in my opinion, one of the most severe has been Le Chatelier, whose pupils are still in predominating places in the French scientific world. Their attitude in respect to Duhem’s contributions is very cold, as I had the opportunity of ascertaining.’

129. The text of the lecture, ‘L’esprit de l’enseignement scientifique,’ was reprinted in P. Langevin, La physique depuis vingr ans (Paris: Librairie Octave Doin, 1923), pp. 424 53. Only the pages relating to Duhem are reproduced in Paul Langevin: La pensLie et l’action, textes recueillis et pri’sentLis par P. Laberenne, pri’faces de Fri’di’ric Joliot Curie et Georges Cogniot (Paris: Editions Sociales, 1946), pp. 60 63, where Lenin’s criticism of Duhem was eagerly recalled!
 
 
 
 

While Langevin could plausibly argue that Duhem’s system could not do justice to new phenomena in physics about which, it may be noted, few had at that time in France a more up to date knowledge than Langevin, he charged unjustly that in Duhem’s system ‘the physicist declares himself satisfied when complex and new phenomena are represented by new terms in the equations, terms whose arbitrary form is indicated only too well by superficial analogies.’ Objectivity was further honored in the breech when Langevin stated that Duhem’s method was a ‘peevish tendency to limit the field of investigation’ and a resolve ‘to declare satisfactory and final a general and superficial knowledge of things, and to forbid ourselves a deeper investigation because a first success yielded some of the more general laws.’

Langevin had no justification for sayin