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Archive for History of Exact Sciences

, Volume 46, Issue 4, pp 341–366 | Cite as

“Will someone say exactly what the H-theorem proves?” A study of Burbury's Condition A and Maxwell's Proposition II

  • Penha Maria Cardoso Dias
Article

Summary

Many historians of science recognize that the outcome of the celebrated debate on Boltzmann's H-Theorem, which took place in the weekly scientific journal Nature, beginning at the end of 1894 and continuing throughout most of 1895, was the recognition of the statistical hypothesis in the proof of the theorem. This hypothesis is the Stosszahlansatz or “hypothesis about the number of collisions.” During the debate, the Stosszahlansatz was identified with another statistical hypothesis, which appeared in Proposition II of Maxwell's 1860 paper; Burbury called it Condition A. Later in the debate, Bryan gave a clear formulation of the Stosszahlansatz. However, the two hypotheses are prima facie different. Burbury interchanged them without justification or even warning his readers. This point deserves clarification, since it touches upon subtle questions related to the foundation of the theory of heat. A careful reading of the arguments presented by Burbury and Bryan in their various invocations of both hypotheses can clarify this technical point. The Stosszahlansatz can be understood in terms of geometrical invariances of the problem of a collision between two spheres. A byproduct of my analysis is a clarification of the debate itself, which is apparently obscure.

Keywords

Clarification Scientific Journal Prima Facie Statistical Hypothesis Technical Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Boltzmann, L. (1872) “Further Studies on the Thermal Equilibrium of Gas Molecules,” translated in S. G. Brush (1965, 1966, 1972), vol. 2, pp. 88–175.Google Scholar
  2. Boltzmann, L. (1877) “On the relation of a General Mechanical Theorem on the Second Law of Thermodynamics,” translated in S. G. Brush (1965, 1966, 1972), vol. 2, pp. 188–202.Google Scholar
  3. Boltzmann, L. (1895a) “On certain questions of the Theory of Gases,” Nature, 51, p. 413.Google Scholar
  4. Boltzmann, L. (1895b) “On the Minimum Theorem in the Theory of Gases,” Nature, 52, p. 221.Google Scholar
  5. Boltzmann, L. (1896) Lectures on Gas Theory, translated by S. G. Brush, University of California Press, Berkeley and Los Angeles, 1964.Google Scholar
  6. Brush, S. G. (ed) (1965, 1966, 1972) Kinetic Theory, 3 vols, Pergamon Press, Oxford.Google Scholar
  7. Brush, S. G. (1976) The Kind of Motion We Call Heat, 2 vols., North-Holland, Amsterdam.Google Scholar
  8. Bryan, G. H. (1891) “Researches Related to the connection of the Second Law with Dynamical Principles,” British Association Report, 61, pp. 85–122.Google Scholar
  9. Bryan, G. H. (1894a) “Report on the Present State of our Knowledge of Thermodynamics,” British Association Report, 64, pp. 64–106.Google Scholar
  10. Bryan, G. H. (1894b) “The Kinetic Theory of Gases,” Nature, 51, p. 176.Google Scholar
  11. Bryan, G. H. (1895) “The Assumption in Boltzmann's Minimum Theorem,” Nature, 52, pp. 29–30.Google Scholar
  12. Burbury, S. H. (1886) “The Foundations of the Kinetic Theory of Gases,” Philosophical Magazine, [5], 21, pp. 481–483.Google Scholar
  13. Burbury, S. H. (1890) “On some Problems in the Kinetic Theory of Gases,” Philosophical Magazine, [5], 30, pp. 298–317.Google Scholar
  14. Burbury, S. H. (1891) “On the Collision of Elastic Bodies,” Abstract, Proceedings of the Royal Society of London, 50, pp. 175–179.Google Scholar
  15. Burbury, S. H. (1892) “On the Collision of Elastic Bodies,” Philosophical Transactions, 183 A, pp. 407–422.Google Scholar
  16. Burbury, S. H. (1894a) “Boltzmann's Minimum Function,” Nature, 51, p. 78–79.Google Scholar
  17. Burbury, S. H. (1894b) “The Kinetic Theory of Gases,” Nature, 51, pp. 175–176.Google Scholar
  18. Burbury, S. H. (1895a) “Boltzmann's Miminum Function,” Nature, 51, p. 320.Google Scholar
  19. Burbury, S. H. (1895b) “Boltzmann's Minimum Function,” Nature, 52, pp. 104–105.Google Scholar
  20. Burbury, S. H. (1904) “On the Theory of Diminishing Entropy,” Philosophical Magazine, [6], 8, pp. 43–49.Google Scholar
  21. Cercignani, C. (1972) “On the Boltzmann Equation for Rigid Spheres,” Transport Theory and Statistical Physics, 2, p. 211–225.Google Scholar
  22. Clausius, R. E. J. (1858) “On the mean lengths of the paths described by the separate molecules of gaseous bodies,” translated by F. Guthrie (1859), republished in S. G. Brush (1965, 1966, 1972), vol. 1, pp. 135–147.Google Scholar
  23. Clausius, R. E. J. (1862) “On the conduction of Heat by Gases,” translated by G. C. Foster (1862) in Philosophical Magazine, [4], 23, pp. 417–435, 512–534.Google Scholar
  24. Culverwell, E. P. (1894a) “Dr. Watson's Proof of Boltzmann's Theorem on Permanence of Distributions,” Nature, 50, p. 617.Google Scholar
  25. Culverwell, E. P. (1894b) “Boltzmann's Minimum Theorem,” Nature, 51, p. 105.Google Scholar
  26. Culverwell, E. P. (1895a) “Boltzmann's Minimum Theorem,” Nature, 51, p. 246.Google Scholar
  27. Culverwell, E. P. (1895b) “Professor Boltzmann's letter on the kinetic theory of Gases,” Nature, 51, p. 581.Google Scholar
  28. Ehrenfest, P. and Ehrenfest T. (1911) The Conceptual Foundations of Statistical Mechanics, translated by M. J. Moravcsik, Cornell University Press, republished by Dover, New York, 1958.Google Scholar
  29. Grad, H. (1958) “Principles of the Kinetic Theory of Gases,” in S. Flügge (ed.), Thermodynamics of Gases, Encyclopaedia of Physics, vol. XII, Springer-Verlag, Berlin, pp. 205–294.Google Scholar
  30. Harris, Stewart (1971) An Introduction to the Theory of the Boltzmann Equation, Holt, Rinehart and Winston, New York.Google Scholar
  31. Klein, M. J. (1973) “The Development of Boltzmnann's Statistical Ideas,” in E. G. D. Cohen & W. Thirring (eds) The Boltzmann Equation: Theory and Applications, Springer-Verlag, Berlin, pp. 53–105.Google Scholar
  32. Kuhn, T. S. (1978) Black-body Theory and the Quantum Discontinuity 1894–1912, Oxford.Google Scholar
  33. Lanford III, O. E. (1975) “Time Evolution of Large Classical Systems,” in J. Moser (ed.) Dynamical Systems, Theory and Applications, Lecture Notes in Physics, 38, Springer-Verlag, Berlin, pp. 1–111.Google Scholar
  34. Maxwell, J. C. (1860) “Illustrations of the Dynamical Theory of Gases,” Philosophical Magazine, [4], 19, pp. 19–32, 20, pp. 21–37. Republished in W. D. Niven (ed.) (1890), vol. 1, pp. 377–409. Also republished in part in S. G. Brush (ed) (1965, 1966, 1972), vol. 1, pp. 148–178.Google Scholar
  35. Maxwell, J. C. (1866) “On the Dynamical Theory of Gases,” Philosophical Transactions of the Royal Society of London, 157, pp. 49–88. Reprinted in W. D. Niven (ed.) (1890), vol. 2, pp. 26–78. Also reprinted in S. G. Brush (ed.) (1965, 1966, 1972), vol. 2. pp. 23–87.Google Scholar
  36. Niven, W. D. (1890) The Scientific Papers of James Clerk Maxwell, 2 vols, Cambridge University Press; republished by Dover, New York, 1961.Google Scholar
  37. Truesdell, C. A. & Muncaster, R. G. (1979) Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas (Treated as a Branch of Rational Mechanics), Academic Press, New York.Google Scholar
  38. Watson, H. W. (1876) A Treatise on the Kinetic Theory of Gases, First Edition, Clarendon, Oxford.Google Scholar
  39. Watson, H. W. (1893) A Treatise on the Kinetic Theory of Gases, Second Edition, Clarendon, Oxford.Google Scholar
  40. Watson, H. W. (1894) “Boltzmann's Minimum Theorem,” Nature, 51, p. 105.Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Penha Maria Cardoso Dias
    • 1
    • 2
  1. 1.Instituto de FísicaUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil
  2. 2.Centro de Lógica, Epistemologia & História da CiênciaUniversidade Estadual de CampinasCampinasBrazil

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