From explanation to description: Molecular and phenomenological theories of piezoelectricity

Historical Studies in the Physical and Biological Sciences

Volumn 34, Issue 1, 2004, Pages 69-94

  Katzir, Shaul ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

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[No Author keywords available]

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EID: 1342284084     PISSN: 08909997     EISSN: None     Source Type: Journal    
DOI: 10.1525/hsps.2003.34.1.69     Document Type: Review

References (115)

1. J.L. Heilbron, A history of the problem of atomic structure from the discovery of the electron to the beginning of quantum mechanics (Ph.D. dissertation, University of California, Berkeley, 1964), 16-24, 41-43, on 42. Later evidence convinced Ostwald by 1909 that "we have experimental proof for the discrete or grainy nature of matter" (ibid., 44).
2. J.L. Heilbron, A history of the problem of atomic structure from the discovery of the electron to the beginning of quantum mechanics (Ph.D. dissertation, University of California, Berkeley, 1964), 16-24, 41-43, on 42. Later evidence convinced Ostwald by 1909 that "we have experimental proof for the discrete or grainy nature of matter" (ibid., 44).
3. Olivier Darrigol, Electrodynamics from Ampère to Einstein (Oxford, 2000), 360-361; Russel McCormmach, "H.A. Lorentz and the electromagnetic view of nature," Isis, 61 (1970), 459-497.
4. Olivier Darrigol, Electrodynamics from Ampère to Einstein (Oxford, 2000), 360-361; Russel McCormmach, "H.A. Lorentz and the electromagnetic view of nature," Isis, 61 (1970), 459-497.
5. Woldemar Voigt, "Phänomenologische und atomistische Betrachtungsweise," in E. Warburg, ed., Die Kultur der Gegenwart, 3:3, vol. 1, Physik (Berlin, 1915), 714-731, on 716.
6. Here the term phenomenological is not restricted to laws but is employed also for theories, and is therefore more general than the usage in Nancy Cartwright, How the laws of physics lie (Oxford, 1983, 1-3). Also, phenomenological theories can be based on various assumptions and principles that are not derived from the empirical data of a specific theory, like the principle of energy conservation and considerations of symmetry.
7. Jacques and Pierre Curie, "Développement par compression de l'électricité polaire dans les cristaux hémièdres à faces inclinées," Société Minéralogique de France, Bulletin, 3 (1880), 90-93; Shaul Katzir, "The discovery of the piezoelectric effect," AHES, 57 (2003), 61-91.
8. Jacques and Pierre Curie, "Développement par compression de l'électricité polaire dans les cristaux hémièdres à faces inclinées," Société Minéralogique de France, Bulletin, 3 (1880), 90-93; Shaul Katzir, "The discovery of the piezoelectric effect," AHES, 57 (2003), 61-91.
9. William Thomson, "On the thermoelectric, thermomagnetic and pyroelectric properties of matter," TMPP, 1, 315-316.
10. Jacques and Pierre Curie, "Sur les phénomènes électriques de la tourmaline des cristaux hémièdres à faces inclinées," OPC, 18-21, on 20.
11. Ibid., 21.
12. Hankel also had theoretical grounds to suppose the existence of a special effect of radiation in his peculiar conception of molecules. Wilhelm Gottlieb Hankel, "Ueber die Entwickelung polarer Elektricität in hemimorphen Krystallen durch Aenderung des Druckes in der Richtung der asymmetrisch ausgebildeten Axen," der Wissenschaften, Leipzig, Berichte, 1880, 144-147; "Über die Aktino- und Piezoelektrischen Eigenschaften des Bergkrystalles und ihre Beziehung zu den Thermoelektrischen," Akademie der Wissenschaften, Leipzig, Mathematisch-Physischen Classe, Abhandlungen, 12 (1881), 459-547; Shaul Katzir, A history of piezoelectricity: The first two decades (Ph.D. dissertation, Tel Aviv University, 2001), 45-47.
13. Hankel also had theoretical grounds to suppose the existence of a special effect of radiation in his peculiar conception of molecules. Wilhelm Gottlieb Hankel, "Ueber die Entwickelung polarer Elektricität in hemimorphen Krystallen durch Aenderung des Druckes in der Richtung der asymmetrisch ausgebildeten Axen," der Wissenschaften, Leipzig, Berichte, 1880, 144-147; "Über die Aktino- und Piezoelektrischen Eigenschaften des Bergkrystalles und ihre Beziehung zu den Thermoelektrischen," Akademie der Wissenschaften, Leipzig, Mathematisch-Physischen Classe, Abhandlungen, 12 (1881), 459-547; Shaul Katzir, A history of piezoelectricity: The first two decades (Ph.D. dissertation, Tel Aviv University, 2001), 45-47.
14. Hankel also had theoretical grounds to suppose the existence of a special effect of radiation in his peculiar conception of molecules. Wilhelm Gottlieb Hankel, "Ueber die Entwickelung polarer Elektricität in hemimorphen Krystallen durch Aenderung des Druckes in der Richtung der asymmetrisch ausgebildeten Axen," der Wissenschaften, Leipzig, Berichte, 1880, 144-147; "Über die Aktino- und Piezoelektrischen Eigenschaften des Bergkrystalles und ihre Beziehung zu den Thermoelektrischen," Akademie der Wissenschaften, Leipzig, Mathematisch-Physischen Classe, Abhandlungen, 12 (1881), 459-547; Shaul Katzir, A history of piezoelectricity: The first two decades (Ph.D. dissertation, Tel Aviv University, 2001), 45-47.
15. Jacques Curie and Charles Friedel, "Sur la pyro-électricité du quartz," Comptes rendus, 96 (1883), 1262-1269, 1390-1395, on 1390-1391, 1393-1394; Wilhelm Röntgen, "Ueber die thermo-, actino- und piézoelectrischen Eigenschaften des Quarzes, AP, 79 (1883), 513-518.
16. Jacques Curie and Charles Friedel, "Sur la pyro-électricité du quartz," Comptes rendus, 96 (1883), 1262-1269, 1390-1395, on 1390-1391, 1393-1394; Wilhelm Röntgen, "Ueber die thermo-, actino- und piézoelectrischen Eigenschaften des Quarzes, AP, 79 (1883), 513-518.
17. Röntgen (ibid.), 515-517; Katzir (ref. 9), 55-57.
18. Röntgen (ibid.), 515-517; Katzir (ref. 9), 55-57.
19. He reported on his molecular assumption seven years later. Wilhelm Röntgen, "Electrische Eigenschaften des Quarzes," AP, 93 (1890) 16-24, on 23; Röntgen (ref. 10), 513.
20. He reported on his molecular assumption seven years later. Wilhelm Röntgen, "Electrische Eigenschaften des Quarzes," AP, 93 (1890) 16-24, on 23; Röntgen (ref. 10), 513.
21. Curie and Friedel (ref. 10). Their hypothesis does not seem simpler than Röntgen's.
22. Curie and Friedel (ref. 10), 1393-1394. On the basis of similar assumptions they demonstrated that uniform heating does not induce an electric effect on additional crystals previously regarded as pyroelectric. "Sur la pyro-éléctricité dans la blend, le chlorate de sodium et la boracite," Comptes rendus, 97 (1883), 61-66.
23. Paul Czermak, "Über der elektrische Verhalten des Quarzes," Mathematisch-Natur-wissenschaftlichen Classe, Akademie der Wissenschaften, Vienna, Sitzungsberichte, 96 (1887), 1217-1244; 97(1888), 301-324, on 1227; Katzir (ref. 9), 64-66.
24. Paul Czermak, "Über der elektrische Verhalten des Quarzes," Mathematisch-Natur-wissenschaftlichen Classe, Akademie der Wissenschaften, Vienna, Sitzungsberichte, 96 (1887), 1217-1244; 97(1888), 301-324, on 1227; Katzir (ref. 9), 64-66.
25. Paul Czermak, "Über der elektrische Verhalten des Quarzes," Mathematisch-Natur-wissenschaftlichen Classe, Akademie der Wissenschaften, Vienna, Sitzungsberichte, 96 (1887), 1217-1244; 97(1888), 301-324, on 1227; Katzir (ref. 9), 64-66.
26. Perhaps Czermak thought that the assumption was independent of a molecular hypothesis, since it does not require one; the logical derivation runs from the molecular hypothesis to his assumptions and not the other way around. Any mechanical assumption that assumes that the electric effect is owing to tension along and only along polar axes would lead to the same result. Nonetheless, historically such an assumption was suggested only with a molecular hypothesis. Röntgen, who referred the effect to inner elastic tension, did not relate it to the polar axes.
27. Czermak (ref. 15), 1218-1234; Jacques and Pierre Curie, "Déformations électriques du quartz," OPC, 30-32, on 31. This paper is the only one of those published in the Comptes rendus that Czermak did not mention.
28. Czermak (ref. 15), 1218-1234; Jacques and Pierre Curie, "Déformations électriques du quartz," OPC, 30-32, on 31. This paper is the only one of those published in the Comptes rendus that Czermak did not mention.
29. The expression for the electric effect in the direction of pressure that follows from Czermak's assumption is close to the expression that follows from valid consideration of symmetry. Here Czermak could find rough confirmation.
30. Wiedemann claimed, without evidence, that pyroelectric crystals cut into two parts do not display electric polarization. Gustav Heinrich Wiedemann, Die Lehere von der Elektricität (2 vols., Braunschweig, 1883), 2, 336-337. The volume went to press before the appearance of Röntgen's, and Curie and Friedel's papers. Still Wiedemann maintained his explanation in the second edition a decade later, 2nd. edn. (1894), 2, 427-429.
31. Pierre Duhem, "Applications de la thermodynamique aux phénomènes thermo-électriques et pyro-électriques," École normale supérieure, Annales scientifiques, 2 (1885), 405-424; 3 (1886), 263-302; Katzir (ref. 9), 97-108.
32. Pierre Duhem, "Applications de la thermodynamique aux phénomènes thermo-électriques et pyro-électriques," École normale supérieure, Annales scientifiques, 2 (1885), 405-424; 3 (1886), 263-302; Katzir (ref. 9), 97-108.
33. Pierre Duhem, "Applications de la thermodynamique aux phénomènes thermo-électriques et pyro-électriques," École normale supérieure, Annales scientifiques, 2 (1885), 405-424; 3 (1886), 263-302; Katzir (ref. 9), 97-108.
34. "Sur les phénomènes piézo-électriques," OPC, 33-34.
35. Pierre Duhem, Leçons sur l'électricité et le magnétisme (3 vols., Paris 1892), 2, 391. The different character of Duhem's two accounts of piezoelectricity points to a development in his view of the aim of scientific theory during the late 1880s to early 1890; Katzir (ref. 9), 106-108, 156-171.
36. Pierre Duhem, Leçons sur l'électricité et le magnétisme (3 vols., Paris 1892), 2, 391. The different character of Duhem's two accounts of piezoelectricity points to a development in his view of the aim of scientific theory during the late 1880s to early 1890; Katzir (ref. 9), 106-108, 156-171.
37. Ernest Mallard, Traité de cristallographie géométrique et physique (2 vols., Paris, 1884), 2, 571.
38. Röntgen (ref. 12), 23; Katzir (ref. 9), 73-76.
39. Röntgen (ref. 12), 23; Katzir (ref. 9), 73-76.
40. Woldemar Voigt, "Allgemeine Theorie der piëzo- und pyroelectrischen Erscheinungen an Krystallen," GA, 36 (1890), 1-99.
41. Ibid., 1.
42. Voigt did not refer to Friedel and Curie's demonstration that uniform pressure does not generate electric effect in crystals like quartz, which they based on the assumption that the effect originates from changes of distance along polar axes. Voigt probably considered their argument invalid since it assumes an independency of the effects in the three non-orthogonal axes. Furthermore, the same kind of assumption led to Czermak's incorrect results.
43. Voigt (ref. 25), 5-6.
44. Voigt was aware that the few examined cases did not prove the universal validity of linearity, and therefore left open the possibility of adding corrections of higher orders if needed. On the verifications see Jacques Pierre and Pierre Curie, "Lois du dégagement de l'électricité par pression dans la tourmaline," OPC, 15-17; Czermak (ref. 15), 1230-1232; Hankel, "Aktino" (ref. 9), 542.
45. Voigt was aware that the few examined cases did not prove the universal validity of linearity, and therefore left open the possibility of adding corrections of higher orders if needed. On the verifications see Jacques Pierre and Pierre Curie, "Lois du dégagement de l'électricité par pression dans la tourmaline," OPC, 15-17; Czermak (ref. 15), 1230-1232; Hankel, "Aktino" (ref. 9), 542.
46. Voigt was aware that the few examined cases did not prove the universal validity of linearity, and therefore left open the possibility of adding corrections of higher orders if needed. On the verifications see Jacques Pierre and Pierre Curie, "Lois du dégagement de l'électricité par pression dans la tourmaline," OPC, 15-17; Czermak (ref. 15), 1230-1232; Hankel, "Aktino" (ref. 9), 542.
47. Woldemar Voigt, "Piezo- und Pyroelectricität, diëlectrische Influenz und Electrostriction bei Krystallen ohne symmetriecentrum," GN (1894), 343-372.
48. y), only six (rather than nine) components of strain are needed.
49. K. Försterling, "Woldemar Voigt zum hundertsten Geburtstage," Die Naturwissenschaften, 38 (1951), 217-221, on 217; Kathryn M. Olesko, Physics as a calling: Discipline and practice in the Königsberg seminar for physics (Ithaca, 1991), 387-388. Olesko's claim, "the problem with this way of thinking was that it inhibited the kinds of thinking needed to achieve theoretical results," does not seem to fit Voigt's theoretical achievement in piezoelectricity.
50. K. Försterling, "Woldemar Voigt zum hundertsten Geburtstage," Die Naturwissenschaften, 38 (1951), 217-221, on 217; Kathryn M. Olesko, Physics as a calling: Discipline and practice in the Königsberg seminar for physics (Ithaca, 1991), 387-388. Olesko's claim, "the problem with this way of thinking was that it inhibited the kinds of thinking needed to achieve theoretical results," does not seem to fit Voigt's theoretical achievement in piezoelectricity.
51. According to Marie Curie, following the publication of Voigt's theory Pierre Curie suspended his plan to publish an analogous theory; Marie Curie, "Préface," OPC, v-xxi, on xiv.
52. British physicists continued to think about molecules and probably also to believe in their existence while preferring phenomenological theories that assumed continuous matter in hydrodynamics. This is another example that the support of analytical theory did not mean a denial of the molecular constitution of matter. Maria Yamalidou, "Molecular ideas in hydrodynamics," Annals of science, 55 (1998), 369-400.
53. Woldemar Voigt, "Theoretische Studien über die Elasticitätverhältnisse der Krystalle." GA (1887), 1-52, and "L'état actuel de nos connaissances sur l'élasticité des cristaux," C.L. Guillaume and L. Poincaré, eds., Rapports présentés au congrès international de physique (Paris, 1900) 1, 277-318, on 289.
54. Woldemar Voigt, "Theoretische Studien über die Elasticitätverhältnisse der Krystalle." GA (1887), 1-52, and "L'état actuel de nos connaissances sur l'élasticité des cristaux," C.L. Guillaume and L. Poincaré, eds., Rapports présentés au congrès international de physique (Paris, 1900) 1, 277-318, on 289.
55. Voigt (ref. 3), 722-723.
56. Ibid., 723, 728. Voigt's argument against the reduction of the physical theory to atoms is very close to the argument of solid state physicists concerning their inability to construct their theories from the behavior of elementary particles. The controversy between "fundamental" physics and the physics of more complex phenomena did not begin with Philip W. Anderson's famous article "More is different: Broken symmetry and the nature of hierarchical structure of science," Science, 177 (1972), 393-396.
57. Ibid., 723, 728. Voigt's argument against the reduction of the physical theory to atoms is very close to the argument of solid state physicists concerning their inability to construct their theories from the behavior of elementary particles. The controversy between "fundamental" physics and the physics of more complex phenomena did not begin with Philip W. Anderson's famous article "More is different: Broken symmetry and the nature of hierarchical structure of science," Science, 177 (1972), 393-396.
58. Eduard Riecke, "Ueber die Pyroelectricität des Turmalins, " AP, 28 (1886), 43-80; "Zwei Fundamentalversuche zur Lehre von der Pyroelectricität," AP, 31 (1887), 889-912; Emil Wiechert, "Eduard Riecke," GN (1916), 45-56, on 48; Woldemar Voigt, "Eduard Riecke als Physiker," Physikalische Zeitschrift, 16 (1915), 219-221; Stanley Goldberg, "Riecke, Eduard," DSB, 11, 445-447; Katzir (ref. 9), 108-112.
59. Eduard Riecke, "Ueber die Pyroelectricität des Turmalins, " AP, 28 (1886), 43-80; "Zwei Fundamentalversuche zur Lehre von der Pyroelectricität," AP, 31 (1887), 889-912; Emil Wiechert, "Eduard Riecke," GN (1916), 45-56, on 48; Woldemar Voigt, "Eduard Riecke als Physiker," Physikalische Zeitschrift, 16 (1915), 219-221; Stanley Goldberg, "Riecke, Eduard," DSB, 11, 445-447; Katzir (ref. 9), 108-112.
60. Eduard Riecke, "Ueber die Pyroelectricität des Turmalins, " AP, 28 (1886), 43-80; "Zwei Fundamentalversuche zur Lehre von der Pyroelectricität," AP, 31 (1887), 889-912; Emil Wiechert, "Eduard Riecke," GN (1916), 45-56, on 48; Woldemar Voigt, "Eduard Riecke als Physiker," Physikalische Zeitschrift, 16 (1915), 219-221; Stanley Goldberg, "Riecke, Eduard," DSB, 11, 445-447; Katzir (ref. 9), 108-112.
61. Eduard Riecke, "Ueber die Pyroelectricität des Turmalins, " AP, 28 (1886), 43-80; "Zwei Fundamentalversuche zur Lehre von der Pyroelectricität," AP, 31 (1887), 889-912; Emil Wiechert, "Eduard Riecke," GN (1916), 45-56, on 48; Woldemar Voigt, "Eduard Riecke als Physiker," Physikalische Zeitschrift, 16 (1915), 219-221; Stanley Goldberg, "Riecke, Eduard," DSB, 11, 445-447; Katzir (ref. 9), 108-112.
62. Eduard Riecke, "Ueber die Pyroelectricität des Turmalins, " AP, 28 (1886), 43-80; "Zwei Fundamentalversuche zur Lehre von der Pyroelectricität," AP, 31 (1887), 889-912; Emil Wiechert, "Eduard Riecke," GN (1916), 45-56, on 48; Woldemar Voigt, "Eduard Riecke als Physiker," Physikalische Zeitschrift, 16 (1915), 219-221; Stanley Goldberg, "Riecke, Eduard," DSB, 11, 445-447; Katzir (ref. 9), 108-112.
63. Eduard Riecke, "Ueber die Pyroelectricität des Turmalins, " AP, 28 (1886), 43-80; "Zwei Fundamentalversuche zur Lehre von der Pyroelectricität," AP, 31 (1887), 889-912; Emil Wiechert, "Eduard Riecke," GN (1916), 45-56, on 48; Woldemar Voigt, "Eduard Riecke als Physiker," Physikalische Zeitschrift, 16 (1915), 219-221; Stanley Goldberg, "Riecke, Eduard," DSB, 11, 445-447; Katzir (ref. 9), 108-112.
64. Eduard Riecke, "Zur Moleculartheorie der piëzoëlectrischen und pyroëlectrischen Erscheinungen," GN (1891), 191-202, on 193; "Molekulartheorie der piëzoelektrischen und pyroelektrischen Erscheinungen," GA, 28 (1892), 1-52.
65. Eduard Riecke, "Zur Moleculartheorie der piëzoëlectrischen und pyroëlectrischen Erscheinungen," GN (1891), 191-202, on 193; "Molekulartheorie der piëzoelektrischen und pyroelektrischen Erscheinungen," GA, 28 (1892), 1-52.
66. Eduard Riecke, "Thermodynamik des Turmalins und mechanische Theorie der Muskelkontraktion," GN (1893), 19-45, on 32.
67. These molecules are not necessarily identical with the chemical molecules. Riecke, GA (ref. 39), 5.
68. Voigt (ref. 38), 220.
69. John G. Burke, Origins of the science of crystals (Berkeley, 1966), 171; Arthur Birembaut, "Bravias, Auguste," DSB, 2, 430-432; Marjorie Senechal, "Brief history of geometrical crystallography," J. Lima-de-Faria, ed., Historical atlas of crystallography (Dordrecht, 1990), 43-59; Paul Forman, "The discovery of the diffraction of x-rays by crystals: A critique of myths," AHES, 6 (1969), 38-71; P.P. Ewald, "The myth of myths: Comments on P. Forman's paper on 'The discovery of the diffraction of x-rays by crystals,'" ibid., 72-83.
70. John G. Burke, Origins of the science of crystals (Berkeley, 1966), 171; Arthur Birembaut, "Bravias, Auguste," DSB, 2, 430-432; Marjorie Senechal, "Brief history of geometrical crystallography," J. Lima-de-Faria, ed., Historical atlas of crystallography (Dordrecht, 1990), 43-59; Paul Forman, "The discovery of the diffraction of x-rays by crystals: A critique of myths," AHES, 6 (1969), 38-71; P.P. Ewald, "The myth of myths: Comments on P. Forman's paper on 'The discovery of the diffraction of x-rays by crystals,'" ibid., 72-83.
71. John G. Burke, Origins of the science of crystals (Berkeley, 1966), 171; Arthur Birembaut, "Bravias, Auguste," DSB, 2, 430-432; Marjorie Senechal, "Brief history of geometrical crystallography," J. Lima-de-Faria, ed., Historical atlas of crystallography (Dordrecht, 1990), 43-59; Paul Forman, "The discovery of the diffraction of x-rays by crystals: A critique of myths," AHES, 6 (1969), 38-71; P.P. Ewald, "The myth of myths: Comments on P. Forman's paper on 'The discovery of the diffraction of x-rays by crystals,'" ibid., 72-83.
72. John G. Burke, Origins of the science of crystals (Berkeley, 1966), 171; Arthur Birembaut, "Bravias, Auguste," DSB, 2, 430-432; Marjorie Senechal, "Brief history of geometrical crystallography," J. Lima-de-Faria, ed., Historical atlas of crystallography (Dordrecht, 1990), 43-59; Paul Forman, "The discovery of the diffraction of x-rays by crystals: A critique of myths," AHES, 6 (1969), 38-71; P.P. Ewald, "The myth of myths: Comments on P. Forman's paper on 'The discovery of the diffraction of x-rays by crystals,'" ibid., 72-83.
73. John G. Burke, Origins of the science of crystals (Berkeley, 1966), 171; Arthur Birembaut, "Bravias, Auguste," DSB, 2, 430-432; Marjorie Senechal, "Brief history of geometrical crystallography," J. Lima-de-Faria, ed., Historical atlas of crystallography (Dordrecht, 1990), 43-59; Paul Forman, "The discovery of the diffraction of x-rays by crystals: A critique of myths," AHES, 6 (1969), 38-71; P.P. Ewald, "The myth of myths: Comments on P. Forman's paper on 'The discovery of the diffraction of x-rays by crystals,'" ibid., 72-83.
74. Riecke, GA (ref. 39), 27-43, Katzir (ref. 12), 115-118.
75. Riecke, GA (ref. 39), 27-43, Katzir (ref. 12), 115-118.
76. Riecke, GA (ref. 39), 43-52, on 50.
77. Eduard Riecke, Lehrbuch der Physik (3rd. edn, Leipzig, 1905), 4.
78. Eduard Riecke and Woldemar Voigt, "Die Piëzoelectrischen Constanten des Quarzes und Turmalines," AP, 45 (1892), 523-552.
79. Katzir (ref. 9), 119.
80. Riecke (ref. 46), 145-155; "Zur Molekularen Theorie der Piezoelektrizität des Tourmaliris," Physikalische Zeitschrift, 13 (1912), 409-415, on 411; and "Pyroelektrizität und Piezoelektrizität," L. Graetz, ed., Handbuch der Elektrizität und des Magnetismus (Leipzig, 1912), 1, 342-420.
81. Riecke (ref. 46), 145-155; "Zur Molekularen Theorie der Piezoelektrizität des Tourmaliris," Physikalische Zeitschrift, 13 (1912), 409-415, on 411; and "Pyroelektrizität und Piezoelektrizität," L. Graetz, ed., Handbuch der Elektrizität und des Magnetismus (Leipzig, 1912), 1, 342-420.
82. Riecke (ref. 46), 145-155; "Zur Molekularen Theorie der Piezoelektrizität des Tourmaliris," Physikalische Zeitschrift, 13 (1912), 409-415, on 411; and "Pyroelektrizität und Piezoelektrizität," L. Graetz, ed., Handbuch der Elektrizität und des Magnetismus (Leipzig, 1912), 1, 342-420.
83. Woldemar Voigt, Lehrbuch der Kristallphysik (Leipzig, 1910), 846-847.
84. In the first shorter communication on his molecular theory, Riecke did not mention the argument about the relative magnitudes of the coefficients (he did not write the expressions for tourmaline coefficients there).
85. Woldemar Voigt, "Beiträge zur molekularen Theorie der Piëzoelectricität," GN (1893), 649-671, 649-651; Katzir (ref. 9), 121-123.
86. Woldemar Voigt, "Beiträge zur molekularen Theorie der Piëzoelectricität," GN (1893), 649-671, 649-651; Katzir (ref. 9), 121-123.
87. Voigt (ref. 52).
88. Ibid., 669-671.
89. The kinetic theory does not agree so well with Voigt's own molecular theory of elasticity, suggested six years earlier. It assumed discrete molecules with a fixed polarity. The internal motion of the atoms in the molecules could be assumed to have only a negligible influence on the molecules. Voigt, "Theoretische" (ref. 35).
90. Woldernar Voigt, "Versuch zur Bestimmung des wahren specifischen electrische Momentes eines Turmalins," AP, 60 (1897), 368-375, on 370.
91. I b i d.
92. Woldemar Voigt, "Lässt sich die Pyroelectricität der Krystalle vollständig auf piëzoelectrische Wirkungen zurückführen?," AP, 66 (1898), 1030-1060, on 1034.
93. Voigt (ref. 30); Katzir (ref. 9), 179-187.
94. Voigt (ref. 30); Katzir (ref. 9), 179-187.
95. Voigt (ref. 58).
96. Lord Kelvin, "On the theory of pyro-electricity and piezo-electricity of crystals," TMPP, 5, 325-332, on 329.
97. Friedrich Pockels, "Ueber die Aenderungen des optischen Verhaltens und die elastischen Deformationen dielektrischer Krystalle im elektrischen Felde," Neues Jahrbuch für Mineralogie, Geologie und Palaeontologie, Beilage-band, 7 (1891), 201-231.
98. Lord Kelvin, "On the piezo-electric property of quartz," TMPP, 5, 311-322. The paper appeared originally in Philosophical magazine of October 1893. It is highly unlikely that Thomson had heard about Voigt's talk.
99. He referred to Voigt's theory in a general lecture in May 1893, "On the molecular tactics of crystal," Baltimore lectures on molecular dynamics and the wave theory of light (London, 1904), Appendix H, 602-642, on 639.
100. Ernest Mallard had suggested nine years earlier a similar explanation based on hypothetical polar molecules, like those assumed by the Curies; Mallard (ref. 23), 559-560.
101. Kelvin (ref. 63), 317-318.
102. Kelvin (ref. 61), 325-326.
103. Ibid., 327-333; Katzir (ref. 9), 134-135.
104. Ibid., 327-333; Katzir (ref. 9), 134-135.
105. Crosbie Smith and M. Norton Wise, Energy and empire: A biographical study of Lord Kelvin (Cambridge, 1989), 463-471.
106. Voigt (ref. 30).
107. On the theoretical elaboration of the phenomenological theory see Katzir (ref. 9), 144-193.
108. None of the essays on pyro- and piezoelectricity in the handbooks mentioned it: Riecke (ref. 49); Friedrich Pockels, "Pyro- and Piezoelectrizität," Adolf Winkelmann ed., Handbuch der Physik (Leipzig, 1905), 4:1, 766-791.
109. None of the essays on pyro- and piezoelectricity in the handbooks mentioned it: Riecke (ref. 49); Friedrich Pockels, "Pyro- and Piezoelectrizität," Adolf Winkelmann ed., Handbuch der Physik (Leipzig, 1905), 4:1, 766-791.
110. Voigt (ref. 38), 220.
111. Voigt (ref. 3), 723.
112. Riecke (ref. 46), 4.
113. Hendrik A. Lorentz, The theory of electrons and its applications to the phenomena of light and radiant heat (2nd ed., New York, 1952), 10-11 (text of 1909, italics in the original).
114. Heilbron (ref. 1), 26-27 and the following discussion.
115. Olivier Darrigol shows that physicists moved with ease from one kind of argument to another in their theories of hydrodynamics and elasticity. Those who preferred continuum-phenomenological theory continued to believe in the molecular structure of matter and to consider it in their arguments. Olivier Darrigol, "Between hydrodynamics and elasticity theory: The first five births of the Navier-Stokes equation," AHES, 56 (2002), 95-150.