Measurement in French Experimental Physics from Regnault to Lippmann. Rhetoric and Theoretical Practice

Summary

This paper explores the legacy of the great French experimental physicist Victor Regnault through the example of Gabriel Lippmann, whose engagement with electrical standardization during the early 1880s was guided by Regnault's methodological precept to measure ‘directly’. Lippmann's education reveals that the theoretical practice of ‘direct’ measurement entailed eliminating extraneous physical effects through the experimental design, rather than, like physicists in Britain and Germany, making numerical ‘corrections’ to measured values. It also provides, paradoxically, exemplars of the qualitative theoretical practices that sustained Regnault's misguided ambition to avoid theory. By considering the largely negative reactions to Lippmann's proposals for selecting suitable electrical units and methods of measuring the ohm, this paper associates these theoretical practices with the ineffectual rhetorical strategies employed by Lippmann to promote his work, and thereby indicates that the practice of direct measurement was limited to French experimental physics. Whilst this result aligns readily with the existence of divergent nineteenth century British and German cultures of precision, it emerges from a very different disciplinary context in which the practice of precision electrical measurement developed independently of submarine telegraphy. This is because, as this paper illustrates, telegraphic engineering and experimental physics remained separate professions in France.

Acknowledgements

I thank Robert Fox and John Heilbron for detailed comments and substantive feedback on several earlier drafts of this paper; Graeme Gooday and Hasok Chang for fruitful discussions; audiences from the School of Philosophy, Religion, and History of Science at the University of Leeds and the Department of Philosophy at the University of Lingnan for comments and suggestions; and the Arts and Humanities Research Council for providing financial support for my doctoral degree, from which this paper was derived.

Notes

¹Bruce Hunt, ‘The Ohm is Where the Art Is: British Telegraph Engineers and the Development of Electrical Standards’, Osiris, 9 (1994), 48–63; Graeme Gooday, ‘Precision Measurement and the Genesis of Physics Teaching Laboratories in Victorian Britain’, British Journal for the History of Science, 23 (1990), 25–51 (32–9); Romualdas Sviedrys, ‘The Rise of Physics Laboratories in Britain’, Historical Studies in the Physical Sciences, 7 (1976), 405–36, especially pages 409–21; Crosbie Smith and Norton Wise, Energy and Empire: A Biographical Study of Lord Kelvin (Cambridge, 1989), 445–63, 649–83. For a brief summary, see Robert Fox and Anna Guagnini, Laboratories, Workshops, and Sites. Concepts and Practices of Research in Industrial Europe, 1800–1914 (Berkeley, 1999), 37–40.

²Christine Blondel, ‘Les Enjeux de la Standardisation en Electricité pour les Français’, in Standardisation and Units in Electricity 1850–1914, edited by Robert Fox (Lancaster, 1989), 25–34; Andrew J. Butrica, ‘Toward the “Pre–history” of Standardisation: Reflections on Electrical Units in France before 1881’, in Standardisation and Units in Electricity, edited by Fox, 3–12; idem, ‘Les Théories Electriques en France 1870–1900: La Contribution des Mathématiciens, des Physiciens et des Ingénieurs à la Construction de la Théorie de Maxwell’ (unpublished doctoral thesis, Ecole des Hautes Etudes en Sciences Sociales, 1992), 112–24. The French university system made an institutional and intellectual division between mathematics and experimental physics that remained unaffected by the rise of theoretical physics during the nineteenth century. See Michel Atten, ‘La Reine Mathématique et sa Petite Soeur’, edited by Bruno Belhoste and others, Les Sciences au Lycée: un Siècle de Réformes des Mathématiques et de la Physique en France et à l'Etranger (Paris, 1996), 45–54 (50–2) and Graeme Gooday and Daniel Jon Mitchell, ‘Rethinking Classical Physics’ in The Oxford Handbook of the History of Physics (Oxford, forthcoming), edited by Robert Fox and Jed Z. Buchwald.

³This was the main reason why Thomson urged the adoption of an absolute system of electrical units upon the British Association Electrical Standards Committee in the 1860s. Hunt, (note 1), 58–60; Smith and Wise (note 1), 687–9. O'Connell suggests that the universalism of a system founded on mechanical work offered the British a means of tacitly asserting their own nationalism. Schaffer also leans towards this view but nonetheless acknowledges the importance of absolute measurement to energy physics. See Joseph O'Connell, ‘Metrology. The Creation of Universality by the Circulation of Particulars’, Social Studies of Science, 23:1 (1993), 129–73 (138–9) and Simon Schaffer, ‘Late Victorian Metrology and its Instrumentation: a Manufactory of Ohms’, edited by Robert Bud and Susan E. Cozzens, Invisible Connections. Instruments, Institutions, and Science (Bellingham, 1992), 23–49 (27–8).

⁴On the irrelevance of an absolute system for electrical practitioners, see Hunt (note 1), 55 and Graeme Gooday, The Morals of Measurement. Accuracy, Irony, and Trust in Late Victorian Electrical Practice (Cambridge, 2004), 10–1. According to Gooday, an absolute system of electrical units only became commercially significant with the domestication of electricity in the 1890s. He describes the rapid triumph of electrical meters based on energy over those based on charge on pages 244–53.

⁵Lippmann postponed a planned determination of the ohm following his appointment in 1883 to the Chair of Mathematical Physics and Probability Theory at the Sorbonne. He returned to experimental research under more favourable circumstances in 1886, when he simultaneously transferred to one of the two professorships in experimental physics and succeeded Jules Jamin as Director of the Physical Research Laboratory. Henri Wuilleumier's determination of the ohm by one of Lippmann's methods was one of the projects under Lippmann's supervision. See Daniel Jon Mitchell, Gabriel Lippmann's Approach to Late–nineteenth Century French Physics (unpublished DPhil thesis, University of Oxford, 2010), 129–34, 144–50, 175–81.

⁶Graeme Gooday agrees with the Victorian physicists Richard Glazebrook and William Shaw that direct comparative measurement was ‘strictly possible only for length and mass’ since time was ascertained from the angular distance traversed on a clock face. Lippmann regarded weight instead of mass as susceptible to direct comparison (see §3). Gooday (note 4), 41–5 (41).

⁷Jean-Baptiste Dumas, ‘Victor Regnault’, in Discours et Eloges Académiques, 2 vols (Paris, 1885), II, 153–200 (170); Victor Regnault, quoted in Paul Langevin, ‘Centenaire de M. Victor Regnault’, Annuaire du Collège de France, 11 (1911), 42–56 (49). Regnault's career and his approach to physics are described and evaluated in Robert Fox, The Caloric Theory of Gases from Lavoisier to Regnault (Oxford, 1971), 295–302, 314–8. For a brief summary of Dumas’ description of Regnault's ‘direct method’, see Matthias Dörries, ‘Easy Transit: Crossing Boundaries Between Physics and Chemistry in mid-Nineteenth Century France’, in Making Space for Science: Territorial Themes in the Shaping of Knowledge, edited by Crosbie Smith and Jon Agar (Basingstoke, 1998), 246–62 (260).

⁸Dumas, ‘Victor Regnault’, 174–5. This technique is also described in Hasok Chang, Inventing Temperature: Measurement and Scientific Progress (Oxford, 2004), 76.

⁹The Cours de Physique of Lippmann's professor of physics at the Lycée Henri IV (then the Lycée Napoléon), Jean-Charles d'Almeida, give little indication that students were introduced to the notion of ‘direct measurement’ during their secondary schooling. See Mitchell (note 5), 9–21. D'Almeida later founded the Société Française de Physique in 1873.

¹⁰Bertin's pupils included the Sorbonne experimental physicists Edmond Bouty, Henri Pellat, and Louis Mouton, the mathematical physicist Marcel Brillouin, and the Provincial physics professors Ernest Bichat, Louis-Alphonse Hurion, and Jules Macé de Lépinay.

¹¹Pierre Bertin, ‘Revue des Travaux de Physique Publiés à l'Etranger’, Annales de Chimie et de Physique, 13 (1868), 436–73 (436); Ernest Lebon, Gabriel Lippmann: Biographie, Bibliographie Analytique des Ecrits (Paris, 1911), 2; Atten (note 2), ‘Les Théories Electriques en France 1870–1900’, 34–5; Mitchell (note 5), 32–40. Bertin only credited Eleuthère Mascart (who succeeded Regnault at the Collège de France) and Eugène Maillot in print, who worked with him in the three volumes of the Annales between 1868 and 1869.

¹²Bertin also questioned the experimental validity of the formula used by Kundt. Pierre Bertin, ‘Nouvelles Déterminations de la Vitesse du Son dans les Tuyaux; par M. Kundt’, Annales de Chimie et de Physique, 4^th ser., 15 (1868), 487–91 (491); Jules Jamin, Cours de Physique de l'Ecole Polytechnique, 1^st edn, 3 vols (1858–66), II (1859), 493–4. Although it appeared in the third and last edition of the Annales for 1868, Bertin's analysis presumably went to press before he had seen Kundt's full publication of his experiments with the ‘double-tube’ apparatus. For a detailed description of the apparatus, the reasons for its construction, and Kundt's other experiments on the speed of sound, see David Cahan, ‘From Dust Figures to the Kinetic Theory of Gases: August Kundt and the Nature of Experimental Physics in the 1860s and 1870s’, Annals of Science, 47:2 (1990), 151–72 (155–60).

¹³Between 1872 and 1875, Lippmann carried out doctoral research on the electro-mechanical properties of mercury electrodes in solution, firstly in Kirchhoff's laboratory in Heidelberg, and then Helmholtz's in Berlin. See Mitchell (note 5), 39–53.

¹⁴Regnault was also forced to make corrections to his determinations of specific heats, but in this instance, he was able to do so via separate trials that aimed to replicate the conditions of the actual experiments as closely as possible. He took this experimental method of correction to be more reliable than theoretical ones, which brought him into conflict with Carl Pape, a former student of Franz Neumann's. Their dispute indicates at least one of the ways in which Regnault's actual practice was idealized in biographies and textbooks. Kathryn Olesko has described how Pape scrutinized every aspect of Regnault's investigation. In Neumann's terms, Regnault's method of correction was based on an ‘interpolation formula’, a raw mathematical generalization of numerical results. Pape judged that since Regnault ‘could not really guarantee the constancy of experimental conditions’, his corrections, and hence his results, were unreliable. Regnault defended his approach by dismissing the mathematical techniques advocated by Pape for making corrections. Olesko explains that Regnault ‘thought he was eliminating extraneous considerations from experimentation by excluding excessive quantification’. Kathryn Olesko, Physics as a Calling. Discipline and Practice in the Königsberg Seminar for Physics (Ithaca and London, 1991), 130–1, 297–8, 378–83 (298, 379).

¹⁵Jules Jamin, Amaury, and Descamps, ‘Sur la Compressibilité des Liquides’, Comptes Rendus Hebdomadaires de l'Académie des Sciences, 66 (1868), 1104–6 (1105). Jamin's method was later deemed to be defective by Charles-Edouard Guillaume. See Jules Jamin and Edmond Bouty, Cours de Physique de l'Ecole Polytechnique, 4^th edn, 4 vols (Paris, 1885–1906), I (1891), 165^*–6^*. The compensation technique based on a duplicate apparatus resembles the more successful procedure devised by Regnault to assess the comparability of different kinds of thermometer, which, as Hasok Chang has explained, constituted a remarkable means of overcoming a vicious circularity in the quantitative measurement of temperature. Chang (note 8), 74–96. See also note 14. On pages 96–102, Chang goes on to assess Regnault's achievements in thermometry and concludes that Regnault ‘was more than just an exceptionally careful and skilled laboratory technician’ because, unlike Dulong and Petit, he approached measurement with ‘philosophical sophistication’ (100, 102).

¹⁶Lippmann, ‘Sur la Mesure de la Résistance Electrique des Liquides au Moyen de l'Electromètre Capillaire’, Comptes Rendus Hebdomadaires de l'Académie des Sciences, 83 (1876), 192–4. Electrolytic polarisation is a complex molecular phenomenon caused by the attraction of ions towards the electrodes. At the time, French textbooks were relatively confident that a hydrogen layer at the negative electrode (‘polarisation by hydrogen’) and an oxygen layer at the positive one (‘polarisation by oxygen’) were somehow responsible, owing to their association with the transportation of charge during electrolysis. See, for example, Jules Jamin, Cours de Physique de l'Ecole Polytechnique, 2^nd edn, 3 vols (Paris, 1863–9), III (1869), 79–88.

¹⁷This multiplicity was formidable. A contributor to La Lumière Electrique reported that ‘there are no less than fifteen units of resistance, seven or eight units of EMF, and five or six units of intensity’. Edouard Hospitalier, ‘De l'Unité dans les Unités’, La Lumière Electrique, 2 (1880), 291. The contemporary literature is also replete with references to various systems of units of different types. These included the ‘electromagnetic system’, the ‘electrostatic system’, the ‘BA system of units’, the ‘CGS system’, ‘Weber's system of absolute electrical units’, and the French ‘système métrique’. Electricians’ different understandings of the relationships and overlap between these systems, as well as the variety of contexts in which they were mentioned, often resulted in confusion.

¹⁸Louis Foucher de Careil, ‘Rapport au Nom de la Comité des Finances’, in Congrès Internationale des Electriciens, Paris 1881. Comptes Rendus des Travaux (Paris, 1882), 13–5 (14); Adolphe Cochery, ‘Rapport au Président de la République’, in Congrès Internationale des Electriciens, 1–3 (2–3); Anonymous, ‘Le Congrès et l'Exposition d'Electricité en 1881’, La Lumière Electrique, 2 (1880), 425–6. On the political and scientific motivation for the 1881 Congress and the suitability of Paris as a location, see Blondel (note 2), 26–32, Robert Fox, ‘Introduction’ in Standardisation and Units in Electricity, edited by Fox, i–v, (ii–iii), Michael Kershaw, ‘The International Electrical Units: a Failure in Standardisation?’, Studies in History and Philosophy of Science, 38 (2007), 108–31 (114), and Atten (note 2), ‘Les Théories Electriques en France’, 132–40.

¹⁹Gabriel Lippmann, Unités Electriques Absolues. Leçons Professées à la Sorbonne 1884–1885, transcribed by A. Berget (Paris, 1899), 1, i. See also Gabriel Lippmann, ‘Les Unités Electriques’, Revue Scientifique de la France et de l'Etranger, 28 (1881), 680–4 (682). Cf. Andrew Gray's popular Absolute Measurements in Electricity and Magnetism (London, 1884), which, notes Schaffer, presented the results of absolute measurements before addressing their theoretical significance. See Schaffer (note 3), 42.

²⁰Gabriel Lippmann, ‘Sur le Choix de l'Unité de Force dans les Mesures Electriques Absolues’, Comptes Rendus Hebdomadaires de l'Académie des Sciences, 92 (1881), 183–6 (186). The development of the CGS system of units was historically complex. It was only definitely articulated in 1873 by the newly-created BA Committee for the Selection and Nomenclature of Dynamical and Electrical Units, which was made up mostly of former members of the disbanded BA Electrical Standards Committee. The Standards Committee had initially adopted the metre as a fundamental unit of length, only for the Nomenclature Committee to replace it with the centimetre. In the interim period, some members of the Standards Committee had gone over to the centimetre independently. See James Clerk Maxwell and Fleeming Jenkin, ‘Second Report. Newcastle-upon-Tyne 1863. Appendix C. On the Elementary Relations between Electrical Measurements’ in Reports of the Committee of Electrical Standards appointed by the British Association for the Advancement of Science (Cambridge, 1913), 86–140 (90) and J. D. Everett, ‘First Report of the Committee for the Selection and Nomenclature of Dynamical and Electrical Units’ in Report of the Forty-Third Meeting of the British Association for the Advancement of Science; held at Bradford in September 1873 (London, 1874), 222–5 (223–4).

²¹Lippmann would have defined M in terms of a force of one (metric) gramme between M and M′ at a distance of one metre. Everett (note 20), 222–5 (223–4); Lippmann (note 19), ‘Les Unités Electriques’, 682. The Reports of the BA Electrical Standards Committee were actually unclear about whether the gramme was a unit of mass or a unit of weight, or somehow both. See, for example, the usage on pages 112, 117, 131–2, 156, and cf. page 152, ‘gramme-weight’, in the ‘Report of the Committee on Standards of Electrical Resistance’ in Report of the Thirty-Third Meeting of the British Association for the Advancement of Science; held at Newcastle-Upon-Tyne in August and September 1863 (London, 1864), 111–76.

²²‘Report of the Committee on Standards of Electrical Resistance’ (note 21), 113–6.

²³Lippmann (note 20), 185. For a static method based on Gauss’ biwire suspension, see Jules Jamin and Edmond Bouty, Cours de Physique de l'Ecole Polytechnique, 3^rd edn, 4 vols (Paris, 1878–83), I (1878), 538–43, and for the method of oscillations, see Lippmann (note 19), Unités Electriques Absolues, 87–8.

²⁴Lippmann's ignorance of the historical development of the BA units is evident from his misattribution of the dyne to the BA Electrical Standards Committee (see note 20). Lippmann (note 20), 183; ‘Report of the Committee on Standards of Electrical Resistance’ (note 21), 112; Smith and Wise (note 1), 687–93. Smith and Wise provide a helpful explanation of the theoretical construction of the absolute electromagnetic system.

²⁵Butrica (note 2) 9–12; Blondel (note 2) 30. Members of the BA Electrical Standards Committee had set aside the British system of units [foot–grain–second] in order to facilitate the acceptance of their new unit of resistance abroad. As Fleeming Jenkin explained in 1865, ‘while there is a possibility that we may accept foreign measures, there is no chance that the Continent will adopt ours.’ Fleeming Jenkin, ‘Report on the New Unit of Electrical Resistance Proposed and Issued by the Committee on Electrical Standards Appointed in 1861 by the British Association’ in Reports of the Committee of Electrical Standards, 277–92 (283). On the lukewarm support of the British government for the metric system, see Terry Quinn, From Artefacts to Atoms. The BIPM and the Search for Ultimate Measurement Standards (Oxford, 2012), 62–3.

²⁸C. Frolich, ‘Des Unités Electriques’, La Lumière Electrique, 2 (1880), 341–3 (342).

²⁶In a review of the decisions made by the Committee on Electrical Units at the 1881 Congress, Lippmann attempted to explain the independence of the BA system of absolute electrical units from the CGS system of mechanical units. He distinguished between the choice of mechanical units as a basis for absolute measurements, and the additional choice between a fundamental unit of either charge (electrostatic system) or current (electromagnetic system) for any absolute system of electrical measurements. Lippmann implied a preference for the electrostatic system, which better suited his electrical expertise. Lippmann (note 19), ‘Les Unités Electriques’, 682.

²⁷Frank Géraldy, ‘Que va Faire le Congrès?’, La Lumière Electrique, 3 (1881), 145–8 (145).

²⁹Frank Géraldy, ‘A Propos des Unités Electriques’, La Lumière Electrique, 3 (1881), 93–4 (93); idem (note 27), 145; Edouard Hospitalier, ‘Système Coordonné des Mesures Electriques de l'Association Brittanique et des Unités Employées en France’, La Lumière Electrique, 1 (1879), 126–8; idem, ‘Des Unités Electriques’, La Lumière Electrique, 2 (1880), 343. On the other hand, contributors freely admitted the difficulties of creating standards for the BA units.

³⁰Lippmann (note 20), 186.

³¹ Lippmann (note 20), 185–6.

³²Frank Géraldy, ‘Un Mot sur les Unités’, La Lumière Electrique, 3 (1881), 89.

³³ Congrès Internationale des Electriciens, 32, 165.

³⁴A handwritten list of invitees to at least one of the clandestine meetings can be found in Les Archives de l'Académie des Sciences, Fonds Dumas, 15.

³⁵ Congrès Internationale des Electriciens, 229, 236–7. For accounts of the unofficial meetings and Mascart's role at the 1881 Congress, see Paul Tunbridge, Lord Kelvin, His Influence on Electrical Measurements and Units (London, 1992), 34–9, and the chapter on ‘Eleuthère Mascart’ in Paul Janet, Notes et Souvenirs (Paris, 1933), 219–74 (259–62). The disciplinary divide between French experimental physics and telegraph engineering revealed by this study transforms Mascart into a more interesting and ambiguous figure in the history of the agreement forged at the 1881 Congress than previously supposed. As a potential intermediary between British energy physics, telegraphy, and French experimental physics, Mascart deserves further study.

³⁶ Congrès Internationale des Electriciens, 230–5, 239–40. Lévy had actually been invited to at least one of the clandestine meetings (see note 34).

³⁷It is possible that Lippmann was attempting to gather German support for a similar attack on the dyne, which suffered from the same problem.

³⁸ Congrès Internationale des Electriciens, 241–3. Several key German players, including Gustav Kirchhoff and Werner Siemens himself, had suggested expressing the metre-long Siemens mercury standard in terms of absolute units back in 1862. Kathryn Olesko, ‘Precision, Tolerance, and Consensus: Local Cultures in German and British Resistance Standards’, in Scientific Credibility and Technical Standards in 19 ^th and early 20 ^th century Germany and Britain, edited by Jed Z. Buchwald (= Archimedes, 1 (1996)), 117–56 (127).

³⁹ Congrès Internationale des Electriciens, 247.

⁴⁰Lippmann (note 19), ‘Les Unités Electriques’, 683–4. Mascart was Regnault's former suppléant (substitute lecturer).

⁴¹Lord Rayleigh and Arthur Schuster, ‘On the Determination of the Ohm in Absolute Measure’, Proceedings of the Royal Society of London, 32 (1881), 104–24 (105). For a more detailed description of the original experiments, see Simon Schaffer, ‘Accurate Measurement is an English Science’ in The Values of Precision, edited by M. Norton Wise, 135–72 (139–41) or idem (note 3), 27–8.

⁴²Rayleigh and Schuster (note 41), 114.

⁴³Gabriel Lippmann, ‘Méthode Expérimentale pour la Détermination de l'Ohm’, Comptes Rendus Hebdomadaires de l'Académie des Sciences, 93 (1881), 713–6.

⁴⁴ Gabriel Lippmann, ‘Méthode Expérimentale pour la Détermination de l'Ohm’, Comptes Rendus Hebdomadaires de l'Académie des Sciences, 93 (1881), 713–6. Since resistance was still calculated from a theoretical formula relating it to these other measured variables, the method appears to remain ‘indirect’. In fact, in this sense, absolute measurements are actually necessarily indirect because the evaluation of electrical quantities in terms of mechanical ones always depends upon mathematical relationships between the two domains. This illustrates reductive measurement, in which the measurement of one quantity is ‘reduced’ to the measurement of another quantity of a different type, rather than compared with a standard of the same type (see note 6). Another example is the measurement of pressure or temperature via the variation in height of a column of fluid. Reductive measurement indeed posed an unacknowledged conceptual challenge to the framework of direct measurement. British commentators were unable to incorporate both forms of measurement into a coherent account. See Gooday (note 4), 42–50. In a second paper, I will describe how Lippmann's experience with the determination of the ohm led to philosophical reflections on measurement that implicitly addressed this challenge.

⁴⁵Marcel Brillouin, ‘Sur la Méthode de M. Lippmann pour la Détermination de l'Ohm’, Comptes Rendus Hebdomadaires de l'Académie des Sciences, 93 (1881), 1069–72 (1069).

⁴⁶Les Archives de l'Académie des Sciences, Marcel Brillouin Dossier.

⁴⁷Marcel Brillouin, ‘Sur la Méthode Expérimentale de M. Lippmann pour la Détermination de l'Ohm’, Comptes Rendus Hebdomadaires de l'Académie des Sciences, 93 (1881), 845–6.

⁴⁸Gabriel Lippmann, ‘Sur la Détermination de l'Ohm: Réponse aux Remarques de M. Brillouin’, Comptes Rendus Hebdomadaires de l'Académie des Sciences, 93 (1881), 955–8 (955–7).

⁴⁹Marcel Brillouin (note 45), 1072.

⁵⁰Les Archives de l'Académie des Sciences, Marcel Brillouin Dossier; Gabriel Lippmann, ‘Sur la Détermination de l'Ohm: Réponse à M. Brillouin’, Comptes Rendus Hebdomadaires de l'Académie des Sciences, 94 (1882), 36–7. According to Lippmann, the magnitude of the induced EMF due to the largest coil was so large that any attempt to set up an opposing EMF in the main circuit would vaporise the resistance. And if the induced EMF was maintained at the same value as for the smallest coil, the required reduction in the rate of rotation would again result in a negligible alteration in the magnitude of the induced EMF.

⁵¹William Ayrton and John Perry, ‘Au Sujet de la Méthode Expérimentale de la Détermination de l'Ohm par M. G. Lippmann’, La Lumière Electrique, 5 (1881), 346–7; Anonymous, ‘On the Absolute Electro-magnetic Units of Resistance and Electro-motive Force, with Suggestions for their Redetermination’, The Telegraphic Journal and Electrical Review, 2:40 (1874), 318–20. As if to rub salt into the wound, a copy of the text of Brillouin's first note on Lippmann's method to the French Academy of Sciences appeared in La Lumière Electrique right beside Ayrton and Perry's letter.

⁵²Gabriel Lippmann, ‘Lettre à M. Le Directeur’, La Lumière Electrique, 6 (1882), 287. Lippmann completely ignored any practical advantages associated with Maxwell's proposal. The reporter for the Telegraphic Journal and Electrical Review had implied that variations in the value of induced EMF over the twenty-degree angular breadth of the commutator would render the indications of the galvanometers unstable. If contact were made only at the position of maximum induced EMF, however (when the coil cut the lines of magnetic force at right angles), the battery circuit could be adjusted to compensate this unique EMF exactly. The galvanoscope y would then remain at zero, and since the secondary circuit ‘would always contain either an equal opposing EMF, or an infinite resistance’, the needle of the tangent galvanometer B would also always remain steady. ‘On the Absolute Electro-magnetic Units of Resistance and Electro-motive Force’ (note 51), 319.

⁵⁴George Carey Foster, ‘Account of Preliminary Experiments on the Determination of Electrical Resistances in Absolute Measure’ in Report of the Fifty-First Meeting of the British Association for the Advancement of Science; held at York in August and September 1881 (London, 1882), 426–31 (431).

⁵³Rayleigh and Schuster (note 41), 105–6; Robert John Strutt, John William Strutt, Third Baron Rayleigh, O.M., F.R.S., Sometime President of the Royal Society and Chancellor of the University of Cambridge (London, 1924), 114–5. Maxwell had identified no fewer than eight corrections to be made to the measured value of R. See James Clerk Maxwell and Fleeming Jenkin, ‘Report of the Committee on Standards of Electrical Resistance: Appendix D. Description of an Experimental Measurement of Electrical Resistance, made at King's College’ in Report of the Thirty-Third Meeting of the British Association for the Advancement of Science, 163–76 (171–3).

⁵⁵ George Carey Foster, ‘Account of Preliminary Experiments on the Determination of Electrical Resistances in Absolute Measure’ in Report of the Fifty-First Meeting of the British Association for the Advancement of Science; held at York in August and September 1881 (London, 1882), 429; Conférence Internationale pour la Détermination des Unités Electriques. Procès-verbaux (Paris, 1882), 36. The reporter for the Telegraphic Journal and Electrical Review explained that ‘the wire whose resistance is to be measured may be of the most convenient form and material for accuracy and constancy, and any wire whatever may be measured just as easily as any other’. Gustav Wiedemann regarded the measurement of the area of the revolving coil the most challenging aspect of the Foster's method, and Maxwell attempted to reassure him by describing a ‘contrivance’ he had devised for the purpose. ‘On the Absolute Electro-magnetic Units of Resistance and Electro-motive Force’ (note 51), 319.

⁵⁶‘Report of the Committee on Standards of Electrical Resistance’ in Report of the Thirty-Third Meeting of the British Association for the Advancement of Science, 119.

⁵⁷Foster (note 54), 431.

⁵⁸Gabriel Lippmann, ‘Sur les Méthodes à Employer pour la Détermination de l'Ohm’, Journal de Physique Théorique et Appliquée, 2^nd ser., 1 (1882), 313–7 (313–4).

⁵⁹Mitchell (note 5), 16–7, 30–1, 37–8, 41–2; Lebon (note 11), 2–3.

⁶⁰James Clerk Maxwell, A Treatise on Electricity and Magnetism, 2 vols (Oxford, 1873), I, 291–3; Gooday (note 4), 183–4; Dominic Jordan, ‘D. E. Hughes, self-induction, and the skin-effect’, Centaurus 26 (1982), 123–153 (139–41). Jordan refers to the skin-effect as a ‘dormant issue’ prior to Hughes’ experiments.

⁶¹Lippmann (note 58), 314–5; idem (note 19), Unités Electriques Absolues, 154–5. More precisely, the magnetic field at each point of the rotating disc had to be evaluated as a function of the dimensions of the fixed coil, which required a series expansion.

⁶²Ludvig Lorenz, ‘Sur les Méthodes à Employer pour la Détermination de l'Ohm’ in Conférence Internationale pour la Détermination des Unités Electriques, 25–8 (25–6).

⁶³ Ludvig Lorenz, ‘Sur les Méthodes à Employer pour la Détermination de l'Ohm’ in Conférence Internationale pour la Détermination des Unités Electriques, 26–7; Lippmann (note 58), 316–7.

⁶⁴Lorenz (note 62), 28.

⁶⁵ Conférence Internationale pour la Détermination des Unités Electriques, 21–3; Les Archives de l'Académie des Sciences, Gabriel Lippmann Dossier, Lippmann to Dumas, 21 September 1882. The proceedings of the meeting contained no apology for Lippmann's absence as would have been customary if he were a delegate. A letter from Mascart to Dumas indicates that the French contingent was being determined about six months before the conference. Lippmann's absence from this list, and his subsequent late invitation, suggest that his involvement remained controversial. Archives de l'Académie des Sciences, Elie Eleuthère Mascart Dossier, Mascart to Dumas, 24 May 1882.

⁶⁶For the sub-committee's meetings, see Conférence Internationale pour la Détermination des Unités Electriques, 29–39, 48–59. For discussion of Lorenz's method, see pages 21, 36–8, 48–9, 53–4, 57–9, 155.

⁶⁷ Conférence Internationale pour la Détermination des Unités Electriques, 48–9; Werner Siemens, ‘Sur une Modification de la Méthode de M. Lorenz’, in Conférence Internationale pour la Détermination des Unités Electriques, 60–2 (61).

⁶⁸ Conférence Internationale pour la Détermination des Unités Electriques, 53. Thomson expressed the absent Rayleigh's preference on his behalf.

⁶⁹ Conférence Internationale pour la Détermination des Unités Electriques, 54. Helmholtz's recommendation exemplified an ‘individualistic’ German culture of standards determination that valued close agreement between the results of many different observers using different methods. See note 80 for a comparison with the British ‘co-operative’ culture.

⁷⁰ Conférence Internationale pour la Détermination des Unités Electriques, 54. Helmholtz's recommendation exemplified an ‘individualistic’ German culture of standards determination that valued close agreement between the results of many different observers using different methods. See note 80 for a comparison with the British ‘co-operative’ culture.

⁷¹ Conférence Internationale pour la Détermination des Unités Electriques, 54. Helmholtz's recommendation exemplified an ‘individualistic’ German culture of standards determination that valued close agreement between the results of many different observers using different methods. See note 80 for a comparison with the British ‘co-operative’ culture, 155.

⁷² Conférence Internationale pour la Détermination des Unités Electriques, 54. Helmholtz's recommendation exemplified an ‘individualistic’ German culture of standards determination that valued close agreement between the results of many different observers using different methods. See note 80 for a comparison with the British ‘co-operative’ culture, 155.

⁷³Lippmann (note 19), Unités Electriques Absolues, 155.

⁷⁴Gabriel Lippmann, ‘Méthode Electrodynamique pour la Détermination de l'Ohm. Mesure Expérimentale de la Constante d'une Bobine Longue’, Comptes Rendus Hebdomadaires de l'Académie des Sciences, 95 (1882), 1348–50. Lippmann nonetheless borrowed practical techniques to overcome other difficulties, for example the regulation of the rate of rotation of the coil. The switch from a disc to a coil changed Lorenz's method from a constant-EMF to a variable-EMF type, like Lippmann's initial method.

⁷⁵ Gabriel Lippmann, ‘Méthode Electrodynamique pour la Détermination de l'Ohm. Mesure Expérimentale de la Constante d'une Bobine Longue’, Comptes Rendus Hebdomadaires de l'Académie des Sciences, 95 (1882), 1348–50. Lippmann nonetheless borrowed practical techniques to overcome other difficulties, for example the regulation of the rate of rotation of the coil. The switch from a disc to a coil changed Lorenz's method from a constant-EMF to a variable-EMF type, like Lippmann's initial method., 1349; Lippmann, Rapport sur l'Ecole Pratique des Hautes Etudes, 1882–3, 17; idem, Titres et Travaux, 2^nd edn (Paris, 1884), 16.

⁷⁶Archives de l'Académie des Sciences, Elie Eleuthère Mascart Dossier, Mascart to Dumas 3 April 1884. Delegates at the 1882 conference had agreed to meet again on the first Monday in October 1883, but several governments had requested additional time to complete experiments. Conférence Internationale pour la Détermination des Unités Electriques, 159–60, 163.

⁷⁷In the two years between the 1882 and 1884 conferences, Mascart, Joubert, Brillouin, and Henri Becquerel had all published their own methods for determining resistance in absolute value.

⁷⁸Kershaw (note 18), 115–6; Larry Lagerström, Constructing Uniformity: the Standardisation of International Electromagnetic Measures 1860–1912 (Unpublished PhD thesis, University of California, Berkeley, 1992), 89–97, 109–15; Conférence Internationale pour la Détermination des Unités Electriques, 55, 67; Conférence Internationale pour la Détermination des Unités Electriques. Deuxième Session (Paris, 1884), 43–6. The length of 106cm resulted from the calculation of a brute average, despite Mascart's observation that determinations based on Lorenz's method had produced the most concordant results. He had tabulated twenty-two values by method, including two of his own. After four deemed clearly unreliable were eliminated, the average became 106.03cm by method and 105.98cm by experiment. Helmholtz proposed to adopt the round number 106cm.

⁷⁹Lippmann's engagement with the standardization of electrical units also suggests interesting Cartesian parallels underlying the framework of direct measurement that merit further exploration. First, he wanted to rethink the conceptual foundations of the necessary measurements for himself, whether this meant the selection of a system of mechanical units or absolute methods of determining the ohm. Historical precedent was of little concern to him. Second, the reliability of a measurement depended upon the selection of an appropriate method. Third, this process necessitated a clear definition of the measured quantity and the distinct separation of physical effects. Cf. Regnault's notion of ‘material realization’ in §2.

⁸⁰Kathryn Olesko has associated Anglo-Germanic differences in the handling of data with opposing social processes governing negotiation over the value of experimental results. The Germans insisted upon the public scrutiny of individual data points produced by independent workers, whereas, as Schaffer has also emphasized, the British reached agreement in private through collaboration, whether within the laboratory or through international networks. They hence tended to report only a summary of their data. Olesko (note 38), 124–31, 137–43; Schaffer (note 41), especially pages 139, 159–64; and also Gooday (note 4), 72–81. Gooday offers an extended account of the metals controversy in terms of ‘trust’ in either liquid or solid metals on pages 82–127.

⁸¹Olesko (note 38), 118. She further notes that ‘telegraphy had the edge in Britain, and physics in Germany’.

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Daniel Jon Mitchell

Winner of the Annals of Science Prize for 2011