Advertisement

“The Etherealization of Common Sense?” Arithmetical and Algebraic Modes of Intelligibility in Late Victorian Mathematics of Measurement

  • Daniel Jon Mitchell
Article
  • 2 Downloads

Abstract

The late nineteenth century gradually witnessed a liberalization of the kinds of mathematical object and forms of mathematical reasoning permissible in physical argumentation. The construction of theories of units illustrates the slow and difficult spread of new “algebraic” modes of mathematical intelligibility, developed by leading mathematicians from the 1830s onwards, into elementary arithmetical pedagogy, experimental physics, and fields of physical practice like telegraphic engineering. A watershed event in this process was a clash that took place during 1878 between J. D. Everett and James Thomson over the meaning and algebraic manipulation of dimensional formulae. This precipitated the emergence of rival “Maxwellian” and “Thomsonian” approaches towards interpreting and applying “dimensional” equations, which expressed the relationship between derived and fundamental units in an absolute system of measurement. What at first looks like a dispute over a seemingly esoteric mathematical tool for unit conversion turns out to concern Everett’s break with arithmetical algebra in the representation and manipulation of physical quantities. This move prompted a vigorous rebuttal from Thomsonian defenders of an orthodox “arithmetical empiricism” on epistemological, semantic, or pedagogical grounds. Their resistance in Victorian Britain to a shift in mathematical intelligibility is suggestive of the difficult birth of theoretical physics, in which the intermediate steps of a mathematical argument need have no direct physical meaning.

Notes

Acknowledgements

I would like to acknowledge the financial support of the Leverhulme Trust (Grant ECF-2013-460) and, through the collaborative project “The Epistemology of the Large Hadron Collider,” the Deutsche Forschungsgemeinschaft (DFG grant FOR 2063). I thank Hasok Chang and members of the Philosophy and History of Physics reading group at the University of Cambridge for detailed discussions of an early draft of this paper, and Sybil de Clark and especially Olivier Darrigol for criticism of the penultimate draft. (The key terminology employed in fact derives from a proposal of Darrigol’s.) I am also grateful to him and to Nadine de Courtenay for inviting me to speak at their Séminaire d’Histoire et Philosophie de Physique (laboratoire SPHERE) in Paris in 2017, and likewise to Jim Grozier for his invitation to present at the workshop “A History of Units 1791–2018” (Teddington, UK, 2016). Audiences on those occasions and at the following conferences or workshops provided constructive feedback: “Measurement at the Crossroads” (Paris, France, 2018), the Seventh International Conference on Integrated History and Philosophy of Science (Hannover, Germany, 2018), and “Beyond the Academy: The Practice of Mathematics from the Renaissance to the Nineteenth Century” (York, UK, 2017). Finally, I am indebted to the archivists at Queen’s College, Belfast, for reproducing selected manuscripts in the James Thomson collection; Janet Hathaway at King’s College, Nova Scotia, for materials on Everett; Peter Holmberg, for supplying his essay on Sundell; and Sloan Evans Despeaux for directing me towards some relevant work in the history of mathematics.

References

  1. 1860. Multiple, submultiple, multiplication. The English Cyclopaedia: A new dictionary of universal knowledge, arts and sciencesvolume 5 (8 Vols, 1859–61), ed. Charles Knight, 820–3. London: Bradbury and Evans.Google Scholar
  2. 1871. New works on mechanics. Nature 5(107): 41–2.Google Scholar
  3. 1872a. Applications for reports and researches not involving grants of money. In Report of the Forty-First Meeting of the British Association for the Advancement of Science; held at Edinburgh in August 1871, lxii–lxxiv. London: John Murray.Google Scholar
  4. 1872b. Sir William Thomson, LL.D., F.R.S., examined. In Royal Commission on Scientific Instruction and the Advancement of Science, Vol. 1, First, Supplementary and Second Reports, with Minutes of Evidence and Appendices, 160–71, §§2652–2873. London: Her Majesty’s Stationery Office.Google Scholar
  5. 1873. Applications for reports and researches not involving grants of money. In Report of the Forty-Second Meeting of the British Association for the Advancement of Science; held at Brighton in August 1872, lvi–lviii. London: John Murray.Google Scholar
  6. 1876. Proceedings of the Physical Society of London. Vol. 1, from 21st March, 1874, to 26th June, 1875. London: Taylor and Francis.Google Scholar
  7. 1879. The British Association Reports: Section F—Economic Science and Statistics. Nature 20(516): 492–3.Google Scholar
  8. 1880. Recommendations of the General Committee for Additional Reports and Researches in Science. In Report of the Fiftieth Meeting of the British Association for the Advancement of Science, Held at Swansea in August and September 1880, lx–lxv. London: John Murray.Google Scholar
  9. 1890. Mechanical units [Suggestions by Professor Everett, November 27th, 1889]. The Engineer 70: 15–16.Google Scholar
  10. A. R. 1925. Andrew Gray—1847–1925. Proceedings of the Royal Society of London A 110: xvi–xix.Google Scholar
  11. A. R. 1927. James Thomson Bottomley—1845–1926. Proceedings of the Royal Society of London A 113: xii–xiii.Google Scholar
  12. A. W. B. 1871. Rodwell’s Dictionary of Science. Nature 3(69): 325–6.Google Scholar
  13. B. L. 1869. Our book shelf: Theoretical and Applied Mechanics by R. Wormell. Nature 1(2): 53–4.Google Scholar
  14. Bishop, Roy L. 1978. Joseph Everett and the King’s College observatory. Journal of the Royal Astronomical Society of Canada 72: 138–148.Google Scholar
  15. Bowers, Brian. 2004. Gordon, James Edward Henry (1852–1893). Oxford dictionary of national biography. http://www.oxforddnb.com/view/article/11057. Accessed 9 Jan 2017.
  16. Bowler, Peter. 2008. James Thomson and the culture of a Victorian engineer. In Kelvin: Life, labours, and legacy, ed. Flood Raymond, Mark McCartney, and Andrew Whitaker, 56–63. Oxford: Oxford University Press.CrossRefGoogle Scholar
  17. Bridgman, Percy. 1951 [1922]. Dimensional analysis. New Haven and London: Yale University Press.Google Scholar
  18. Brock, William. 1975. Geometry and the universities: Euclid and his modern rivals 1860–1901. History of Education 4(2): 21–35.CrossRefGoogle Scholar
  19. Brock, William. 2000. Who were they? Richard Wormell (1838–1914). School Science Review 81(297): 93–97.Google Scholar
  20. Brock, William. 2004. Wormell, Richard (1838–1914). Oxford dictionary of national biography. http://www.oxforddnb.com/view/article/40970. Accessed 9 Jan 2017.
  21. Brook-Smith, J. 1910 [1881]. Arithmetic in theory and practice, 6th edn. Macmillan and Co.Google Scholar
  22. Bryant, Margaret. 1986. The London experience of secondary education. London: The Athlone Press.Google Scholar
  23. Bryce, James. 1872. Treatise on Algebra, 4th ed. Edinburgh: Adam and Charles Black.Google Scholar
  24. Buchwald, Jed Z. 1985. From Maxwell to microphysics: Aspects of electromagnetic theory in the last quarter of the nineteenth century. Chicago: University of Chicago Press.Google Scholar
  25. Buchwald, Jed Z., and Sungook Hong. 2003. Physics. In From natural philosophy to the sciences, ed. David Cahan, 163–195. London: University of Chicago Press.Google Scholar
  26. Cajori, Florian. 1917. A history of elementary mathematics, with hints on methods of teaching. Revised and enlarged edition. New York: The Macmillan Company.zbMATHGoogle Scholar
  27. Carroll, Lewis [Dodgson, Charles]. 1998 [1865/1872]. Alice’s adventures in Wonderland, and Through the looking-glass. London: Penguin Books.Google Scholar
  28. Clifford, William Kingdon. 1878. Elements of dynamic: An introduction to the study of motion and rest in solid and fluid bodies. London: Macmillan & Co.Google Scholar
  29. Corry, Leo. 2015. A brief history of numbers. Oxford: Oxford University Press.zbMATHGoogle Scholar
  30. Crowe, Michael. 1985 [1967]. A history of vector analysis: The evolution of the idea of a vectorial system. New York: Dover.Google Scholar
  31. Cumming, Linneaus. 1876. An introduction to the theory of electricity, with numerous examples. London: Macmillan and Co.Google Scholar
  32. Cumming, Linneaus. 1885. An introduction to the theory of electricity, with numerous examples, 3rd ed. London: Macmillan and Co.Google Scholar
  33. de Boer, Jan. 1994/5. On the history of quantity calculus and the international system. Metrologia 31: 405–29.CrossRefGoogle Scholar
  34. de Clark, Sybil Gertrude. 2010. L’analyse dimensionnelle en France et en Grande-Bretagne au XIXe siècle. Ph.D. dissertation, Université Paris Diderot (Paris 7).Google Scholar
  35. de Clark, Sybil Gertrude. 2016. The dimensions of the magnetic pole: A controversy at the heart of early dimensional analysis. Archive for History of Exact Sciences 70: 293–324.CrossRefGoogle Scholar
  36. de Clark, Sybil Gertrude. 2017. Qualitative vs quantitative conceptions of homogeneity in nineteenth century dimensional analysis. Annals of Science 74(4): 299–325.CrossRefGoogle Scholar
  37. de Courtenay, Nadine. 2015. The double interpretation of the equations of physics and the quest for common meanings. In Standardization in measurement, ed. Oliver Schlaudt and Lara Huber, 53–68. London: Pickering and Chatto.Google Scholar
  38. de Morgan, Augustus. 1840. The elements of arithmetic, 4th ed. London: Taylor and Walton.Google Scholar
  39. Denniss, John. 2008. Learning arithmetic: Textbooks and their users in England 1500–1900. In The Oxford handbook of the history of mathematics, ed. Eleanor Robson and Jacqueline Stedall, 448–467. Oxford: Oxford University Press.Google Scholar
  40. Despeaux, Sloan Evans. 2002. The development of a publication community: Nineteenth-century mathematics in British scientific journals. Ph.D. dissertation, University of Virginia.Google Scholar
  41. Despeaux, Sloan Evans. 2011. A voice for mathematics: Victorian mathematical journals and societies. In Mathematics in Victorian Britain, ed. Raymond Flood, Adrian Rice, and Robin Wilson, 155–174. Oxford: Oxford University Press.Google Scholar
  42. Elwick, James. 2014. Economies of scales: Evolutionary naturalists and the Victorian examination system. In Victorian scientific naturalism: Community, identity, continuity, 131–56. Chicago: University of Chicago Press.Google Scholar
  43. Everett, Joseph David. 1860. Essay on mathematical study. The Calendar of King’s College, Windsor, Nova Scotia, 51–6. Halifax, N.S.: James Bowes and Sons.Google Scholar
  44. Everett, Joseph David. 1872. On units of force and energy [Abstract]. Report of the Forty-First Meeting of the British Association for the Advancement of Science; held at Edinburgh in August 1871, 29. London: John Murray.Google Scholar
  45. Everett, Joseph David. 1874a. Letter to James Thomson, 15th Dec 1874. MS.13.M.6.b. Queen’s College Archives, Belfast.Google Scholar
  46. Everett, Joseph David. 1874b. Letter to James Thomson, 21st Dec 1874. MS.13.M.6.c. Queen’s College Archives, Belfast.Google Scholar
  47. Everett, Joseph David. 1874c. 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, 222–5. London: John Murray.Google Scholar
  48. Everett, Joseph David. 1875a. Illustrations of the centimetre-gramme-second system of units. London: Taylor and Francis.Google Scholar
  49. Everett, Joseph David. 1875b. Letter to James Thomson, 25th March 1875. MS.13.K.1.a. Queen’s College Archives, Belfast.Google Scholar
  50. Everett, Joseph David. 1875c. Second report of the Committee for the Selection and Nomenclature of Dynamical and Electrical Units. In Report of the Forty-Fourth Meeting of the British Association for the Advancement of Science; held at Belfast in August 1874, 255. London: John Murray.Google Scholar
  51. Everett, Joseph David. 1878. Letter to James Thomson, 24th July 1878. MS.13.M.6.g. Queen’s College Archives, Belfast.Google Scholar
  52. Everett, Joseph David. 1879. Units and physical constants. London: Macmillan and Co.Google Scholar
  53. Everett, Joseph David. 1886. Units and physical constants, 2nd ed. London: Macmillan and Co.Google Scholar
  54. Falconer, Isobel. 2014. Cambridge and building the Cavendish laboratory. In James Clerk Maxwell: Perspectives on his life and work, ed. Raymond Flood, Mark McCartney, and Andrew Whitaker, 67–99. Oxford: Oxford University Press.Google Scholar
  55. Ferguson, Robert M. 1882. Electricity. New edition revised and extended by James Blyth, M.A., F.R.S.E. London and Edinburgh: W & R. Chambers.Google Scholar
  56. G. A. G. and R. A. H. 1926. Andrew Gray. Proceedings of the Royal Society of Edinburgh 45(4): 373–7.CrossRefGoogle Scholar
  57. Gauss, Charles Frédéric [Carl Friedrich]. 1834. Mesure absolue de l’intensité du magnetisme terrestre. Annales de Physique et de Chimie, 57: 5–69.Google Scholar
  58. Gladstone, John Hall. 1876. Report of the Council. In Proceedings of the Physical Society of London. Vol. 1, from 21st March, 1874, to 26th June, 1875, 13–6. London: Taylor and Francis.Google Scholar
  59. Glazebrook, Richard Tetley, and William Napier Shaw. 1885. Practical physics. New York: D. Appleton and Co.Google Scholar
  60. Glazebrook, Richard Tetley and Shaw, William Napier. 1904 [1893]. Practical physics. New impression [of 4th edition]. London, New York, and Bombay: Longmans, Green, and Co.Google Scholar
  61. Gooday, Graeme. 2000. “Lies, damned lies and declinism: Lyon Playfair, the Paris 1867 Exhibition and the contested rhetorics of scientific education and industrial performance. In The golden age: Essays in British social and economic history, 1850–1870, ed. Ian Inkster, Colin Griffin, Jeff Hill, and Judith Rowbotham, 105–120. Aldershot: Ashgate.Google Scholar
  62. Gooday, Graeme. 2004. The morals of measurement. Accuracy, irony, and trust in Late Victorian electrical practice. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  63. Gordon, James. 1880. A physical treatise on electricity and magnetism. London: Sampson Low et al.Google Scholar
  64. Gray, Andrew. 1884. Absolute measurements in electricity and magnetism. London: Macmillan and Co.zbMATHGoogle Scholar
  65. Gray, Andrew. 1888–93. The theory and practice of absolute measurement in electricity and magnetism, 2nd edn (2 Vols). London: Macmillan and Co.Google Scholar
  66. Gray, Andrew. 1921. Absolute measurements in electricity and magnetism, 2nd ed. London: Macmillan and Co.zbMATHGoogle Scholar
  67. Holmberg, Peter. 1988. August Fredrik Sundell—Fysiker, Matematiker och Astronom. Arkhimedes 40: 19–30.MathSciNetGoogle Scholar
  68. Hunger Parshall, Karen. 2011. Victorian algebra: The freedom to create new mathematical entities. In Mathematics in Victorian Britain, ed. Raymond Flood, Adrian Rice, and Robin Wilson, 339–358. Oxford: Oxford University Press.Google Scholar
  69. Hunt, Bruce J. 1994. The ohm is where the art is: British telegraph engineers and the development of electrical standards. Osiris 9: 48–63.CrossRefGoogle Scholar
  70. Hunt, Bruce J. 2005 [1991]. The Maxwellians. Ithaca and London: Cornell University Press.Google Scholar
  71. Hunt, Bruce J. 2015. Maxwell, measurement, and the modes of electromagnetic theory. Historical Studies in the Natural Sciences 45(2): 303–339.CrossRefGoogle Scholar
  72. J[ohn], P[erry]. 1904. Obituary notices of fellows deceased. Proceedings of the Royal Society of London 75: 377–380.Google Scholar
  73. Jenkin, Fleeming. 1887. A fragment of truth. In Papers literary, scientific, &c. by the late Fleeming Jenkin, Vol. 1 (2 Vols), ed. Sidney Colvin and J. A. Ewing. London: Longmans, Green, and Co.Google Scholar
  74. Heilbron, John L. 1993. A mathematicians’ mutiny, with morals. In World changes: Thomas Kuhn and the nature of science, ed. Paul Horwich, 81–129. Cambridge: MIT Press.Google Scholar
  75. Kaiser, David. 2005. Introduction: Moving pedagogy from the periphery to the center. In Pedagogy and the practice of science: Historical and contemporary perspectives, ed. David Kaiser, 1–8. Cambridge: MIT Press.Google Scholar
  76. Kim, Dong-Won. 2002. Leadership and creativity: A history of the Cavendish laboratory 18711919 [Archimedes 5]. Dordrecht/Boston/London: Kluwer.Google Scholar
  77. King Bidwell, James. 2013. The teaching of arithmetic in England from 1550 until 1800 as influenced by social change. In The European mathematical awakening: A journey through the history of mathematics from 1000 to 1800, ed. Frank J. Swetz, 76–81. Mineola, New York: Dover.Google Scholar
  78. Kohlrausch, Friedrich. 1874. An introduction to physical measurements, with appendices on absolute electrical measurement, etc., trans. Thomas Hutchinson Waller and Henry Richardson Proctor. New York: D. Appleton and Co.Google Scholar
  79. Kuhn, Thomas. 1977. Preface. The essential tension. Selected studies in scientific tradition and change, ix–xxiii. Chicago: University of Chicago Press.Google Scholar
  80. Kuhn, Thomas. 2012 [1962]. The structure of scientific revolutions, 4th edn. Chicago: University of Chicago Press.Google Scholar
  81. Koppelman, Elaine. 1971. The calculus of operations and the rise of abstract algebra. Archive for History of Exact Sciences 8(3): 155–242.MathSciNetCrossRefGoogle Scholar
  82. Kyburg Jr., Henry E. 1997. Quantities, magnitudes, and numbers. Philosophy of Science 64(3): 377–410.MathSciNetCrossRefGoogle Scholar
  83. [“Larmor and Bottomley”]. 1912. Biographical sketch. In Collected papers in physics and engineering by James Thomson, D.Sc., LL.D, F.R.S., selected and arranged by Sir Joseph Larmor and James Thomson, M.A., xiii–xci. Cambridge: Cambridge University Press.Google Scholar
  84. Lees, Charles Herbert. 1912. Everett, Joseph David. In Dictionary of national biography: Supplement, January 1901–December 1911, ed. Sir Sidney Lee, 638–9. [S.I.]: Smith, Elder, and Co.Google Scholar
  85. Lees, Charles Herbert [revised by Graeme J. N. Gooday]. 2004. Everett, Joseph David (1831–1904). Oxford dictionary of national biography. http://www.oxforddnb.com/view/article/33049. Accessed 9 Jan 2017.
  86. [“Letters”]. 1888. Letters referring to the proposed emendation. In Association for the Improvement of Geometrical Teaching. Fourteenth General Report, January 1888, 60–70. Bedford: W. J. Robinson.Google Scholar
  87. Lindley, David. 2004. Degrees Kelvin: A tale of genius, invention, and tragedy. Washington: Joseph Henry Press.Google Scholar
  88. Lodge, Alfred. 1888. The multiplication and division of concrete quantities. In Association for the Improvement of Geometrical Teaching. Fourteenth General Report, January 1888, 47–60. Bedford: W. J. Robinson.Google Scholar
  89. Longair, Malcolm. 2016. Maxwell’s enduring legacy: A scientific history of the Cavendish laboratory. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  90. Macleod, Roy M. 1971. The support of Victorian science: The endowment of research movement in Great Britain, 1868–1900. Minerva 9(2): 197–230.CrossRefGoogle Scholar
  91. Martins, Roberto de A. 1981. The origin of dimensional analysis. Journal of the Franklin Institute 311: 331–337.MathSciNetCrossRefGoogle Scholar
  92. Maxwell, James Clerk. 1871. Presidential address. In Report of the Fortieth Meeting of the British Association for the Advancement of Science; Held at Liverpool in September 1870. London: John Murray.Google Scholar
  93. Maxwell, James Clerk. 1872. Theory of heat, 3rd ed. London: Longmans, Green, and Co.Google Scholar
  94. Maxwell, James Clerk. 1873. A treatise on electricity and magnetism, 2 Vols. Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  95. Maxwell, James Clerk. 1890 [1871]. Remarks on the mathematical classification of physical quantities. In The scientific papers of James Clerk Maxwell, Vol. 2 (2 Vols), ed. W. D. Niven, 257–66. Cambridge: Cambridge University Press.Google Scholar
  96. Maxwell, James Clerk. 1990 [1865]. Letter to William Thomson, 17 and 18 April 1865. In The scientific letters and papers of James Clerk Maxwell, Vol. 1 (3 Vols, 1990–2002), ed. Peter Harman, 218–20. Cambridge: Cambridge University Press.Google Scholar
  97. Maxwell, James Clerk. 2002 [1877]. On dimensions. In The scientific letters and papers of James Clerk Maxwell, Vol. 3 (3 Vols, 1990–2002), ed. Peter Harman, 517–20. Cambridge: Cambridge University Press.Google Scholar
  98. Maxwell, James Clerk and Jenkin, Fleeming. 1864. Appendix C—On the elementary relations between electrical measurements, 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, 59–96. London: John Murray.Google Scholar
  99. Maxwell, James Clerk and Jenkin, Fleeming. 1865. Appendix C—On the elementary relations between electrical measurements. Philosophical Magazine, 4th series 4(29): 436–60, 507–25.Google Scholar
  100. Maxwell, James Clerk, and Fleeming Jenkin. 1873. Appendix C—On the elementary relations between electrical measurements. In Reports of the Committee on Electrical Standards appointed by the British Association for the Advancement of Science, ed. Fleeming Jenkin, 59–96. London: E. & F. N. Spon.Google Scholar
  101. Mitchell, Daniel Jon. 2017a. Making sense of absolute measurement. James Clerk Maxwell, Fleeming Jenkin, William Thomson, and the construction of the dimensional formula. Studies in History and Philosophy of Modern Physics 58: 63–79.CrossRefGoogle Scholar
  102. Mitchell, Daniel Jon. 2017b. What’s nu? A re-examination of Maxwell’s “ratio-of-units” argument, from the mechanical theory of the electromagnetic field to “On the elementary relations between electrical measurements”. Studies in History and Philosophy of Science 65–66: 87–98.CrossRefGoogle Scholar
  103. Mitchell, Daniel Jon. Forthcoming. The dynamics of the masses: Absolute measurement and elementary physics pedagogy in Victorian Britain, 1863–1879. History of Science. Google Scholar
  104. Nahin, Paul J. 1988. Oliver Heaviside: Sage in solitude. The life, work and times of an electrical genius of the Victorian age. New York: IEEE Press.Google Scholar
  105. Olesko, Kathryn. 2005. The foundations of a canon: Kohlrausch’s Practical Physics. In Pedagogy and the practice of science. Historical and contemporary perspectives, ed. David Kaiser, 324–356. Cambridge: MIT Press.Google Scholar
  106. Price, Michael. 1986. The Perry movement in school mathematics. In The development of the secondary curriculum, ed. Michael Price, 103–155. London: Croom Helm.Google Scholar
  107. Pycior, Helena M. 1981. George Peacock and the British origins of symbolical algebra. Historica Mathematica 8: 23–45.MathSciNetCrossRefGoogle Scholar
  108. Pycior, Helena M. 1982. Early criticism of the symbolical approach to algebra. Historica Mathematica 9: 392–412.MathSciNetCrossRefGoogle Scholar
  109. Pycior, Helena M. 1983. Augustus de Morgan’s algebraic work: The three stages. Isis 74(2): 211–226.MathSciNetCrossRefGoogle Scholar
  110. Pycior, Helena M. 1989. At the intersection of mathematics and humor: Lewis Carroll’s Alices and symbolical algebra. In Energy and entropy: Science and culture in Victorian Britain, ed. Patrick Brantlinger. Bloomington: Indiana University Press.Google Scholar
  111. Richards, Joan L. 1980. The art and science of British algebra: A study in the perception of mathematical truth. Historica Mathematica 7: 343–365.MathSciNetCrossRefGoogle Scholar
  112. Richards, Joan L. 1987. Augustus de Morgan, the history of mathematics, and the foundations of algebra. Isis 78(1): 6–30.MathSciNetCrossRefGoogle Scholar
  113. Richards, Joan L. 2011. “This compendious language:” Mathematics in the world of Augustus de Morgan. Isis 102(3): 506–510.MathSciNetCrossRefGoogle Scholar
  114. Roche, John. 1998. The mathematics of measurement: A critical history. London: The Athlone Press.zbMATHGoogle Scholar
  115. Schaffer, Simon. 1992. Late Victorian metrology and its instrumentation: A manufactory of Ohms. In Invisible Connections: Instruments, institutions, and science [Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), Vol. 10309], ed. Robert Bud and Susan E. Cozzens, 23–51. Bellingham, WA: SPIE Optical Engineering Press.Google Scholar
  116. Schaffer, Simon. 1997. Metrology, metrication, and Victorian values. In Victorian science in context, ed. Bernard Lightman, 438–474. Chicago: University of Chicago Press.Google Scholar
  117. [“Second Report”]. 1864. 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, 111–176. London: John Murray.Google Scholar
  118. Simon, Josep. 2012. Secondary matters: Textbooks and the making of physics in nineteenth-century France and England. History of Science 1: 339–374.CrossRefGoogle Scholar
  119. Smith, Crosbie. 1998. The science of energy. Chicago: University of Chicago Press.Google Scholar
  120. Smith, Crosbie. 2004. Thomson, James (1822–1892). Oxford dictionary of national biography. http://www.oxforddnb.com/view/article/27312. Accessed 9 Jan 2017.
  121. Smith, Crosbie, and Norton Wise. 1989. Energy and empire: A biographical study of Lord Kelvin. Cambridge: Cambridge University Press.Google Scholar
  122. Sundell, August Fredrick. 1882. Remarks on absolute systems of physical units. Philosophical Magazine 14(86): 81–109.Google Scholar
  123. T[hompson], S[ilvanus] P. 1881. Our book shelf: Natural Philosophy for London University Matriculation by Edward B. Aveling. Nature 25(630): 76–7.Google Scholar
  124. Thomson, James [Sr]. 1825. A treatise on arithmetic in theory and practice, 2nd edn. Belfast: Simms and McIntyre.Google Scholar
  125. Thomson James [Sr]. 1880. A treatise on arithmetic in theory and practice, 72nd edn edited by his sons James Thomson and Sir William Thomson. London: Longmans, Green, and Co.Google Scholar
  126. Thomson, James. Undated manuscript. MS.13.K.1.e. Queen’s College Archives, Belfast.Google Scholar
  127. Thomson, James. 1878. Letter to William Thomson, 19th July 1878. MS.13.M.41.f. Queen’s College Archives, Belfast.Google Scholar
  128. Thomson, James. 1912 [1878]. On dimensional equations, and on some verbal expressions in numerical science. In Collected papers in physics and engineering by James Thomson, D.Sc., LL.D, F.R.S., selected and arranged by Sir Joseph Larmor and James Thomson, M.A., 375–9. Cambridge: Cambridge University Press.Google Scholar
  129. Thomson, William. 1889 [1883]. The six gateways of knowledge. In Popular Lectures and Addresses, Vol. 1 (3 Vols, 1889–94), 253–99. London: Macmillan and Co.Google Scholar
  130. Thomson, William, and Peter Guthrie Tait. 1867. Treatise on Natural Philosophy. Oxford: Clarendon Press.zbMATHGoogle Scholar
  131. Thomson, William, and Peter Guthrie Tait. 1879. Treatise on natural philosophy, 2nd ed. Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  132. Thomson Bottomley, James. 1912 [1893]. Obituary notice. In Collected papers in physics and engineering by James Thomson, D.Sc., LL.D, F.R.S., selected and arranged by Sir Joseph Larmor and James Thomson, M.A., xcii–cii. Cambridge: Cambridge University Press.Google Scholar
  133. Timmons, George. 2001. Science and science education in schools after the Great Exhibition. Endeavour 25(3): 109–120.CrossRefGoogle Scholar
  134. Warwick, Andrew. 2003. Masters of theory: Cambridge and the rise of mathematical physics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  135. Warwick, Andrew, and David Kaiser. 2005. Conclusion: Kuhn, Foucault, and the power of pedagogy. In Pedagogy and the practice of science: Historical and contemporary perspectives, ed. David Kaiser, 393–409. Cambridge: MIT Press.Google Scholar
  136. Williams, W. 1892. On the relation of the dimensions of physical quantities to directions in space. Philosophical Magazine 22(146): 234–271.zbMATHGoogle Scholar
  137. Wormell, Richard. 1871a. Elementary geometry. Nature 4(100): 425.CrossRefGoogle Scholar
  138. Wormell, Richard. 1871b. Wormell’s mechanics. Nature 5(108): 63.CrossRefGoogle Scholar
  139. Wormell, Richard. 1876. The principles of dynamics: An elementary textbook for science students. London: Rivingtons.Google Scholar
  140. Wormell, Richard. 1887. The principles of dynamics: An elementary text-book for science students, 2nd ed. London: Rivingtons.Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Theoretical Physics and CosmologyRWTH AachenAachenGermany

Personalised recommendations