The contributions of J.J. Sylvester, F.R.S., to mechanics and mathematical physics

Notes and Records of the Royal Society

Volumn 55, Issue 2, 2001, Pages 253-265

  Grattan Guinness, I ^a  

^a MIDDLESEX UNIVERSITY   (United Kingdom)

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[No Author keywords available]

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EID: 0042262582     PISSN: 00359149     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsnr.2001.0142     Document Type: Article

References (112)

1. P.A. MacMahon, Proc. R. Soc. Lond. 63, ix-xxv (pp. xii, xviii and xx-xxi). H.F. Baker (ed.), 'Biographical notice'. In J.J. Sylvester, Collected mathematical papers, 4 vols (Cambridge University Press, 1904-1912), vol. 4, pp. xv-xxxvii. This edition is cited below as 'CMP'.
2. P.A. MacMahon, Proc. R. Soc. Lond. 63, ix-xxv (pp. xii, xviii and xx-xxi). H.F. Baker (ed.), 'Biographical notice'. In J.J. Sylvester, Collected mathematical papers, 4 vols (Cambridge University Press, 1904-1912), vol. 4, pp. xv-xxxvii. This edition is cited below as 'CMP'.
3. After Sylvester's death the Jewish community in Britain and the USA raised funds to establish a medal in his name to be awarded by The Royal Society to eminent mathematicians: see I. Grattan-Guinness, 'The Sylvester Medal: origins and recipients 1901-1949', Notes Rec. R. Soc. Lond. 47, 105-108 (1992).
4. K.H. Parshall (ed.), James Joseph Sylvester; life and work in letters (Oxford University Press, 1998). The papers on applied mathematics are not discussed in the letters selected. Parshall is now undertaking a biography. R.C. Archibald provides several kinds of valuable data, especially in 'Unpublished letters of James Joseph Sylvester and other information concerning his life and work', Osiris 1, 85-154, starting with a career vita and list of secondary literature on pp. 88-95. My colleague Tony Crilly has completed one on Cayley, on whom the literature is also sparse; however, Cayley's relationship with Sylvester did not concern itself much with applied mathematics, though he was strongly interested in aspects of mechanics.
5. K.H. Parshall (ed.), James Joseph Sylvester; life and work in letters (Oxford University Press, 1998). The papers on applied mathematics are not discussed in the letters selected. Parshall is now undertaking a biography. R.C. Archibald provides several kinds of valuable data, especially in 'Unpublished letters of James Joseph Sylvester and other information concerning his life and work', Osiris 1, 85-154, starting with a career vita and list of secondary literature on pp. 88-95. My colleague Tony Crilly has completed one on Cayley, on whom the literature is also sparse; however, Cayley's relationship with Sylvester did not concern itself much with applied mathematics, though he was strongly interested in aspects of mechanics.
6. It is not possible to summarize this vast range of developments; for details and many further references, see I. Grattan-Guinness. Convolutions in French mathematics, 1800-1840. From the calculus and mechanics to mathematical analysis and mathematical physics, 3 vols (Basel, Birkhäuser; Berlin, Deutscher Verlag der Wissenschaften, 1990). Other general literature on French science at this time includes M.P. Crosland, The Society of Arcueil (London, Heinemann, 1967); his Science under control. The French Academy of Sciences 1795-1914 (Cambridge University Press, 1992); and R. Fox and G. Weisz (eds), The organisation of science and technology in France 1808-1914 (Cambridge University Press, 1980). On applied mathematics and physics in general at this time, see E. Garber, The language of physics, the calculus and the development of theoretical physics in Europe, 1750-1914 (Boston, Birkhäuser, 1999); and J.J. Roche, The mathematics of measurement (London, Athlone Press, 1998), esp. ch. 7-10. Some aspects of the physical sciences in Britain are treated in C. Smith, The science of energy. A cultural history of energy in physics in Victorian Britain (London, Athlone Press, 1998), although the treatment of mechanics is light.
7. It is not possible to summarize this vast range of developments; for details and many further references, see I. Grattan-Guinness. Convolutions in French mathematics, 1800-1840. From the calculus and mechanics to mathematical analysis and mathematical physics, 3 vols (Basel, Birkhäuser; Berlin, Deutscher Verlag der Wissenschaften, 1990). Other general literature on French science at this time includes M.P. Crosland, The Society of Arcueil (London, Heinemann, 1967); his Science under control. The French Academy of Sciences 1795-1914 (Cambridge University Press, 1992); and R. Fox and G. Weisz (eds), The organisation of science and technology in France 1808-1914 (Cambridge University Press, 1980). On applied mathematics and physics in general at this time, see E. Garber, The language of physics, the calculus and the development of theoretical physics in Europe, 1750-1914 (Boston, Birkhäuser, 1999); and J.J. Roche, The mathematics of measurement (London, Athlone Press, 1998), esp. ch. 7-10. Some aspects of the physical sciences in Britain are treated in C. Smith, The science of energy. A cultural history of energy in physics in Victorian Britain (London, Athlone Press, 1998), although the treatment of mechanics is light.
8. It is not possible to summarize this vast range of developments; for details and many further references, see I. Grattan-Guinness. Convolutions in French mathematics, 1800-1840. From the calculus and mechanics to mathematical analysis and mathematical physics, 3 vols (Basel, Birkhäuser; Berlin, Deutscher Verlag der Wissenschaften, 1990). Other general literature on French science at this time includes M.P. Crosland, The Society of Arcueil (London, Heinemann, 1967); his Science under control. The French Academy of Sciences 1795-1914 (Cambridge University Press, 1992); and R. Fox and G. Weisz (eds), The organisation of science and technology in France 1808-1914 (Cambridge University Press, 1980). On applied mathematics and physics in general at this time, see E. Garber, The language of physics, the calculus and the development of theoretical physics in Europe, 1750-1914 (Boston, Birkhäuser, 1999); and J.J. Roche, The mathematics of measurement (London, Athlone Press, 1998), esp. ch. 7-10. Some aspects of the physical sciences in Britain are treated in C. Smith, The science of energy. A cultural history of energy in physics in Victorian Britain (London, Athlone Press, 1998), although the treatment of mechanics is light.
9. It is not possible to summarize this vast range of developments; for details and many further references, see I. Grattan-Guinness. Convolutions in French mathematics, 1800-1840. From the calculus and mechanics to mathematical analysis and mathematical physics, 3 vols (Basel, Birkhäuser; Berlin, Deutscher Verlag der Wissenschaften, 1990). Other general literature on French science at this time includes M.P. Crosland, The Society of Arcueil (London, Heinemann, 1967); his Science under control. The French Academy of Sciences 1795-1914 (Cambridge University Press, 1992); and R. Fox and G. Weisz (eds), The organisation of science and technology in France 1808-1914 (Cambridge University Press, 1980). On applied mathematics and physics in general at this time, see E. Garber, The language of physics, the calculus and the development of theoretical physics in Europe, 1750-1914 (Boston, Birkhäuser, 1999); and J.J. Roche, The mathematics of measurement (London, Athlone Press, 1998), esp. ch. 7-10. Some aspects of the physical sciences in Britain are treated in C. Smith, The science of energy. A cultural history of energy in physics in Victorian Britain (London, Athlone Press, 1998), although the treatment of mechanics is light.
10. It is not possible to summarize this vast range of developments; for details and many further references, see I. Grattan-Guinness. Convolutions in French mathematics, 1800-1840. From the calculus and mechanics to mathematical analysis and mathematical physics, 3 vols (Basel, Birkhäuser; Berlin, Deutscher Verlag der Wissenschaften, 1990). Other general literature on French science at this time includes M.P. Crosland, The Society of Arcueil (London, Heinemann, 1967); his Science under control. The French Academy of Sciences 1795-1914 (Cambridge University Press, 1992); and R. Fox and G. Weisz (eds), The organisation of science and technology in France 1808-1914 (Cambridge University Press, 1980). On applied mathematics and physics in general at this time, see E. Garber, The language of physics, the calculus and the development of theoretical physics in Europe, 1750-1914 (Boston, Birkhäuser, 1999); and J.J. Roche, The mathematics of measurement (London, Athlone Press, 1998), esp. ch. 7-10. Some aspects of the physical sciences in Britain are treated in C. Smith, The science of energy. A cultural history of energy in physics in Victorian Britain (London, Athlone Press, 1998), although the treatment of mechanics is light.
11. It is not possible to summarize this vast range of developments; for details and many further references, see I. Grattan-Guinness. Convolutions in French mathematics, 1800-1840. From the calculus and mechanics to mathematical analysis and mathematical physics, 3 vols (Basel, Birkhäuser; Berlin, Deutscher Verlag der Wissenschaften, 1990). Other general literature on French science at this time includes M.P. Crosland, The Society of Arcueil (London, Heinemann, 1967); his Science under control. The French Academy of Sciences 1795-1914 (Cambridge University Press, 1992); and R. Fox and G. Weisz (eds), The organisation of science and technology in France 1808-1914 (Cambridge University Press, 1980). On applied mathematics and physics in general at this time, see E. Garber, The language of physics, the calculus and the development of theoretical physics in Europe, 1750-1914 (Boston, Birkhäuser, 1999); and J.J. Roche, The mathematics of measurement (London, Athlone Press, 1998), esp. ch. 7-10. Some aspects of the physical sciences in Britain are treated in C. Smith, The science of energy. A cultural history of energy in physics in Victorian Britain (London, Athlone Press, 1998), although the treatment of mechanics is light.
12. It is not possible to summarize this vast range of developments; for details and many further references, see I. Grattan-Guinness. Convolutions in French mathematics, 1800-1840. From the calculus and mechanics to mathematical analysis and mathematical physics, 3 vols (Basel, Birkhäuser; Berlin, Deutscher Verlag der Wissenschaften, 1990). Other general literature on French science at this time includes M.P. Crosland, The Society of Arcueil (London, Heinemann, 1967); his Science under control. The French Academy of Sciences 1795-1914 (Cambridge University Press, 1992); and R. Fox and G. Weisz (eds), The organisation of science and technology in France 1808-1914 (Cambridge University Press, 1980). On applied mathematics and physics in general at this time, see E. Garber, The language of physics, the calculus and the development of theoretical physics in Europe, 1750-1914 (Boston, Birkhäuser, 1999); and J.J. Roche, The mathematics of measurement (London, Athlone Press, 1998), esp. ch. 7-10. Some aspects of the physical sciences in Britain are treated in C. Smith, The science of energy. A cultural history of energy in physics in Victorian Britain (London, Athlone Press, 1998), although the treatment of mechanics is light.
13. See I. Grattan-Guinness, 'The ingénieur savant, 1800-1830: a neglected figure in the history of French mathematics and science', Science in Context 6, 405-433 (1993).
14. See I. Grattan-Guinness, 'End of dominance: the diffusion of French mathematics elsewhere, 1820-1870'. In K.H. Parshall and A.C. Rice (eds), Mathematics unbound: the evolution of an international mathematical community (2001). (In the press.)
15. The historiography of these changes is rather distorted by attention only to the Analytical Society. For a wider survey, see N. Guiccciardini, The development of Newtonian calculus in Britain 1700-1800 (Cambridge University Press, 1989), Part 3.
16. For a survey of many of these developments see P. Harman (ed.), Wranglers and physicists. Cambridge physics in the nineteenth century (Manchester University Press, 1985); and more scatteredly in E.T. Whittaker, History of the theories of aether and electricity. The classical theories, 2nd edn (London, Nelson, 1951), esp. ch. 4-9passim.
17. For a survey of many of these developments see P. Harman (ed.), Wranglers and physicists. Cambridge physics in the nineteenth century (Manchester University Press, 1985); and more scatteredly in E.T. Whittaker, History of the theories of aether and electricity. The classical theories, 2nd edn (London, Nelson, 1951), esp. ch. 4-9passim.
18. P. Kelland, 'On the laws of transmission of light in crystallized media'. Trans. Camb. Phil. Soc. 6, 323-360 (1838); 'On the laws of transmission of light and heat in uncrystallized media', Phil. Mag. (3)10, 336-342 (1837).
19. P. Kelland, 'On the laws of transmission of light in crystallized media'. Trans. Camb. Phil. Soc. 6, 323-360 (1838); 'On the laws of transmission of light and heat in uncrystallized media', Phil. Mag. (3)10, 336-342 (1837).
20. J.J. Sylvester, 'Analytical development of Fresnel's theory of crystals'. Phil. Mag. (3)11, 461-469, 537-541 (1837), (3)12, 73-83 (1837); and succeeding 'Notes', (3)12, 341-345 (1837). Together in CMP, vol. 1, pp. 1-27 (quote on Hamilton on p. 19).
21. J.J. Sylvester, 'Analytical development of Fresnel's theory of crystals'. Phil. Mag. (3)11, 461-469, 537-541 (1837), (3)12, 73-83 (1837); and succeeding 'Notes', (3)12, 341-345 (1837). Together in CMP, vol. 1, pp. 1-27 (quote on Hamilton on p. 19).
22. J.J. Sylvester, 'Analytical development of Fresnel's theory of crystals'. Phil. Mag. (3)11, 461-469, 537-541 (1837), (3)12, 73-83 (1837); and succeeding 'Notes', (3)12, 341-345 (1837). Together in CMP, vol. 1, pp. 1-27 (quote on Hamilton on p. 19).
23. J.J. Sylvester, 'Analytical development of Fresnel's theory of crystals'. Phil. Mag. (3)11, 461-469, 537-541 (1837), (3)12, 73-83 (1837); and succeeding 'Notes', (3)12, 341-345 (1837). Together in CMP, vol. 1, pp. 1-27 (quote on Hamilton on p. 19).
24. J. J. Sylvester, 'On the motion and rest of fluids', Phil. Mag. (3)13, 449-453 (1838); also in CMP, vol. 1, pp. 28-32. He mentioned 'recent papers' there by Ivory, presumably including 'On the conditions of equilibrium of a homogeneous planet in a fluid state', (3)13, 81-82 (1838). On Ivory's career, see A.D.D. Craik, 'James Ivory, F.R.S., mathematician', Notes Rec. R. Soc. Lond. 54, 223-247 (2000).
25. J. J. Sylvester, 'On the motion and rest of fluids', Phil. Mag. (3)13, 449-453 (1838); also in CMP, vol. 1, pp. 28-32. He mentioned 'recent papers' there by Ivory, presumably including 'On the conditions of equilibrium of a homogeneous planet in a fluid state', (3)13, 81-82 (1838). On Ivory's career, see A.D.D. Craik, 'James Ivory, F.R.S., mathematician', Notes Rec. R. Soc. Lond. 54, 223-247 (2000).
26. J. J. Sylvester, 'On the motion and rest of fluids', Phil. Mag. (3)13, 449-453 (1838); also in CMP, vol. 1, pp. 28-32. He mentioned 'recent papers' there by Ivory, presumably including 'On the conditions of equilibrium of a homogeneous planet in a fluid state', (3)13, 81-82 (1838). On Ivory's career, see A.D.D. Craik, 'James Ivory, F.R.S., mathematician', Notes Rec. R. Soc. Lond. 54, 223-247 (2000).
27. J. J. Sylvester, 'On the motion and rest of fluids', Phil. Mag. (3)13, 449-453 (1838); also in CMP, vol. 1, pp. 28-32. He mentioned 'recent papers' there by Ivory, presumably including 'On the conditions of equilibrium of a homogeneous planet in a fluid state', (3)13, 81-82 (1838). On Ivory's career, see A.D.D. Craik, 'James Ivory, F.R.S., mathematician', Notes Rec. R. Soc. Lond. 54, 223-247 (2000).
28. C.F. Gauss, 'Über ein neues allgemeines Grundgesetz in der Mechanik: "Die Bewegung eines Systems, materieller, auf was immer für eine Art unter sich verknüpter Punkte, deren Bewegung zugleich an was immer für äussere Beschränkungen gebunden sind, geschieht in jedem Augenblick in möglich grösster Übereinstimmung mit der freien Bewegung, oder unter möglich kleinsten Zwange, in dem man als Mass des Zwanges, den das ganze System in jeden Zeittheilchen erleidet, die Summe der Produkte aus dem Quadrate der Ablenkung jedes Punktes von seiner freien Bewegung in seiner Masse betrachtet"', Journal für die reine und angewandte Mathematik 4, 232-235 (1829); also in Werke, vol. 5 (Leipzig, Teubner, 1877), pp. 23-28. His principle attracted a modest measure of interest during the century; see P. Stäckel, 'Bemerkungen zum Prinzip des kleinsten Zwanges'. Sitzungsberichte der Heidelbergsche Akademie der Wissenschaften, mathematisch-physikalische Klasse, paper no. 11 (1919).
29. C.F. Gauss, 'Über ein neues allgemeines Grundgesetz in der Mechanik: "Die Bewegung eines Systems, materieller, auf was immer für eine Art unter sich verknüpter Punkte, deren Bewegung zugleich an was immer für äussere Beschränkungen gebunden sind, geschieht in jedem Augenblick in möglich grösster Übereinstimmung mit der freien Bewegung, oder unter möglich kleinsten Zwange, in dem man als Mass des Zwanges, den das ganze System in jeden Zeittheilchen erleidet, die Summe der Produkte aus dem Quadrate der Ablenkung jedes Punktes von seiner freien Bewegung in seiner Masse betrachtet"', Journal für die reine und angewandte Mathematik 4, 232-235 (1829); also in Werke, vol. 5 (Leipzig, Teubner, 1877), pp. 23-28. His principle attracted a modest measure of interest during the century; see P. Stäckel, 'Bemerkungen zum Prinzip des kleinsten Zwanges'. Sitzungsberichte der Heidelbergsche Akademie der Wissenschaften, mathematisch-physikalische Klasse, paper no. 11 (1919).
30. C.F. Gauss, 'Über ein neues allgemeines Grundgesetz in der Mechanik: "Die Bewegung eines Systems, materieller, auf was immer für eine Art unter sich verknüpter Punkte, deren Bewegung zugleich an was immer für äussere Beschränkungen gebunden sind, geschieht in jedem Augenblick in möglich grösster Übereinstimmung mit der freien Bewegung, oder unter möglich kleinsten Zwange, in dem man als Mass des Zwanges, den das ganze System in jeden Zeittheilchen erleidet, die Summe der Produkte aus dem Quadrate der Ablenkung jedes Punktes von seiner freien Bewegung in seiner Masse betrachtet"', Journal für die reine und angewandte Mathematik 4, 232-235 (1829); also in Werke, vol. 5 (Leipzig, Teubner, 1877), pp. 23-28. His principle attracted a modest measure of interest during the century; see P. Stäckel, 'Bemerkungen zum Prinzip des kleinsten Zwanges'. Sitzungsberichte der Heidelbergsche Akademie der Wissenschaften, mathematisch-physikalische Klasse, paper no. 11 (1919).
31. J.J. Sylvester, 'Remark on the foregoing', Phil. Mag. (3)14, 47-48 (1839); also in CMP, vol. 1, p. 39.
32. J.J. Sylvester, 'Remark on the foregoing', Phil. Mag. (3)14, 47-48 (1839); also in CMP, vol. 1, p. 39.
33. S. Earnshaw, Dynamics, 1st edn (Cambridge, Deighton, 1832), pp. 76-77.
34. J.J. Sylvester, 'On the 'motion and rest of rigid bodies', Phil. Mag. (3)14, 188-190 (1839); also in CMP, vol. 1, pp. 33-35.
35. J.J. Sylvester, 'On the 'motion and rest of rigid bodies', Phil. Mag. (3)14, 188-190 (1839); also in CMP, vol. 1, pp. 33-35.
36. M. Ostrogradsky, 'A singular case of the equilibrium of incompressible fluids', Taylor's Scientific Memoirs 1, 548-554 (1837); original French version in Mémoires de l'Académie Royale des Sciences de Saint-Pétersbourg (6)3 pt 1, 333-340 (1838). In his first paper (op. cit., note 11) Sylvester also mentioned B. Pratt, 'Remarks' on that paper in Phil. Mag. (3)12, 385-386 (1838).
37. M. Ostrogradsky, 'A singular case of the equilibrium of incompressible fluids', Taylor's Scientific Memoirs 1, 548-554 (1837); original French version in Mémoires de l'Académie Royale des Sciences de Saint-Pétersbourg (6)3 pt 1, 333-340 (1838). In his first paper (op. cit., note 11) Sylvester also mentioned B. Pratt, 'Remarks' on that paper in Phil. Mag. (3)12, 385-386 (1838).
38. M. Ostrogradsky, 'A singular case of the equilibrium of incompressible fluids', Taylor's Scientific Memoirs 1, 548-554 (1837); original French version in Mémoires de l'Académie Royale des Sciences de Saint-Pétersbourg (6)3 pt 1, 333-340 (1838). In his first paper (op. cit., note 11) Sylvester also mentioned B. Pratt, 'Remarks' on that paper in Phil. Mag. (3)12, 385-386 (1838).
39. J.J. Sylvester, 'On definite double integration...', Phil. Mag. (3)14, 298-300 (1839); also in CMP, vol. 1, pp. 36-38.
40. J.J. Sylvester, 'On definite double integration...', Phil. Mag. (3)14, 298-300 (1839); also in CMP, vol. 1, pp. 36-38.
41. On this context, see especially J.J. Cross, 'Integral theorems in Cambridge mathematical physics, 1830-1855'. In Harman, op. cit., note 8, pp. 112-148.
42. Information from The Royal Society's Archives. His 12 supporters included Herschel and Powell, and also the physicist Charles Wheatstone.
43. J. Barrow-Green, '"A corrective to the spirit of too exclusively pure mathematics": Robert Smith (1689-1768) and his prizes at Cambridge University', Annls Sci. 56, 271-316 (1999).
44. L.S. Feuer, 'America's first Jewish professor: James Joseph Sylvester at the University of Virginia'. Am. Jewish Arch. 36, 151-201 (1984).
45. G.G. Stokes, 'Note on the axis of instantaneous rotation'. Cambridge and Dublin Math. J. 3, 128-130 (1848); not in his Papers.
46. J.J. Sylvester, 'On the rotation of a rigid body', Phil. Mag. (3)37, 440-444 (1850); also in CMP, vol. 1, pp. 157-161.
47. J.J. Sylvester, 'On the rotation of a rigid body', Phil. Mag. (3)37, 440-444 (1850); also in CMP, vol. 1, pp. 157-161.
48. O. Rodrigues, 'Des lois géométriques qui régissent les déplacements d'un système solide dans l'espace...', Journal des Mathématiques Pures et Appliquées (1)5, 380-440 (1840). See J.J. Gray, 'Olinde Rodrigues' paper on transformation groups', Arch. Hist. Exact Sci. 21, 375-385 (1980). The relationship between Rodrigues's and Sylvester's theorems is explained in E.J. Routh, The elementary part of a treatise on the dynamics of the system of rigid bodies, 7th edn (London, Macmillan, 1905), pp. 223-226. On the dynamical prehistory, see P. Dupont, 'Esame storico-critico del contributo di d'Alembert, Eulero, Poisson, Poncelet ed altari al concetto dell'asse istantaneo di rotazone nei moti rigidi con un punto fisso'. Atti dell'Accademia di Scienze di Torino, classe di scienze fisiche matematiche e naturali 98, 537-572 (1963).
49. O. Rodrigues, 'Des lois géométriques qui régissent les déplacements d'un système solide dans l'espace...', Journal des Mathématiques Pures et Appliquées (1)5, 380-440 (1840). See J.J. Gray, 'Olinde Rodrigues' paper on transformation groups', Arch. Hist. Exact Sci. 21, 375-385 (1980). The relationship between Rodrigues's and Sylvester's theorems is explained in E.J. Routh, The elementary part of a treatise on the dynamics of the system of rigid bodies, 7th edn (London, Macmillan, 1905), pp. 223-226. On the dynamical prehistory, see P. Dupont, 'Esame storico-critico del contributo di d'Alembert, Eulero, Poisson, Poncelet ed altari al concetto dell'asse istantaneo di rotazone nei moti rigidi con un punto fisso'. Atti dell'Accademia di Scienze di Torino, classe di scienze fisiche matematiche e naturali 98, 537-572 (1963).
50. O. Rodrigues, 'Des lois géométriques qui régissent les déplacements d'un système solide dans l'espace...', Journal des Mathématiques Pures et Appliquées (1)5, 380-440 (1840). See J.J. Gray, 'Olinde Rodrigues' paper on transformation groups', Arch. Hist. Exact Sci. 21, 375-385 (1980). The relationship between Rodrigues's and Sylvester's theorems is explained in E.J. Routh, The elementary part of a treatise on the dynamics of the system of rigid bodies, 7th edn (London, Macmillan, 1905), pp. 223-226. On the dynamical prehistory, see P. Dupont, 'Esame storico-critico del contributo di d'Alembert, Eulero, Poisson, Poncelet ed altari al concetto dell'asse istantaneo di rotazone nei moti rigidi con un punto fisso'. Atti dell'Accademia di Scienze di Torino, classe di scienze fisiche matematiche e naturali 98, 537-572 (1963).
51. O. Rodrigues, 'Des lois géométriques qui régissent les déplacements d'un système solide dans l'espace...', Journal des Mathématiques Pures et Appliquées (1)5, 380-440 (1840). See J.J. Gray, 'Olinde Rodrigues' paper on transformation groups', Arch. Hist. Exact Sci. 21, 375-385 (1980). The relationship between Rodrigues's and Sylvester's theorems is explained in E.J. Routh, The elementary part of a treatise on the dynamics of the system of rigid bodies, 7th edn (London, Macmillan, 1905), pp. 223-226. On the dynamical prehistory, see P. Dupont, 'Esame storico-critico del contributo di d'Alembert, Eulero, Poisson, Poncelet ed altari al concetto dell'asse istantaneo di rotazone nei moti rigidi con un punto fisso'. Atti dell'Accademia di Scienze di Torino, classe di scienze fisiche matematiche e naturali 98, 537-572 (1963).
52. J.J. Sylvester, 'Sur l'involution des lignes droites dans l'espace considérées comme des axes de rotation' and 'Note sur l'involution de six lignes dans l'espace. Comptes rendus de l'Académie des Sciences 52, 741-746 and 815-817 (1861); also in CMP, vol. 2, pp. 236-241.
53. J.J. Sylvester, 'Sur l'involution des lignes droites dans l'espace considérées comme des axes de rotation' and 'Note sur l'involution de six lignes dans l'espace. Comptes rendus de l'Académie des Sciences 52, 741-746 and 815-817 (1861); also in CMP, vol. 2, pp. 236-241.
54. On this and other institutions for higher education in London, see A.C. Rice, 'Mathematics in the metropolis: a survey of Victorian London', Historia Mathematica 23, 376-417 (1996).
55. J.J. Sylvester, 'A trifle on projectiles', Phil. Mag. (4)11, 450-453 (1856); also in CMP, vol. 2, pp. 55-58.
56. J.J. Sylvester, 'A trifle on projectiles', Phil. Mag. (4)11, 450-453 (1856); also in CMP, vol. 2, pp. 55-58.
57. J.J. Sylvester, 'Letter on Professor Galbraith's construction for the range of projectiles'. Phil. Mag. (4)12, 112-113 (1856); also in CMP, vol. 2, pp. 61-62.
58. J.J. Sylvester, 'Letter on Professor Galbraith's construction for the range of projectiles'. Phil. Mag. (4)12, 112-113 (1856); also in CMP, vol. 2, pp. 61-62.
59. W.J.M. Rankine, 'On the stability of loose earth', Phil. Trans. R. Soc. Lond. 147, 9-28 (1857); summary in Proc. R. Soc. Lond. 8, 185-187 (1856-57); neither in his Papers. Of earlier French work Sylvester seemed to know only that by Coulomb and not the later contributions of de Prony, J.F. Français and Poncelet; on all this see Grattan-Guinness, op. cit., note 4, pp. 543-548, 1260.
60. W.J.M. Rankine, 'On the stability of loose earth', Phil. Trans. R. Soc. Lond. 147, 9-28 (1857); summary in Proc. R. Soc. Lond. 8, 185-187 (1856-57); neither in his Papers. Of earlier French work Sylvester seemed to know only that by Coulomb and not the later contributions of de Prony, J.F. Français and Poncelet; on all this see Grattan-Guinness, op. cit., note 4, pp. 543-548, 1260.
61. W.J.M. Rankine, 'On the stability of loose earth', Phil. Trans. R. Soc. Lond. 147, 9-28 (1857); summary in Proc. R. Soc. Lond. 8, 185-187 (1856-57); neither in his Papers. Of earlier French work Sylvester seemed to know only that by Coulomb and not the later contributions of de Prony, J.F. Français and Poncelet; on all this see Grattan-Guinness, op. cit., note 4, pp. 543-548, 1260.
62. J.J. Sylvester, 'On the pressure of earth on revetment walls', Phil. Mag. (4)20, 488-499 (1860); also in CMP, vol. 2, pp. 215-224.
63. J.J. Sylvester, 'On the pressure of earth on revetment walls', Phil. Mag. (4)20, 488-499 (1860); also in CMP, vol. 2, pp. 215-224.
64. Sylvester's paper is not mentioned in the fine survey in F.W.F. Kötter, 'Die Entwicklung der Lehre vom Erddruck'. Jahresbericht der Deutschen Mathematiker-Vereinigung 2, 77-154 (1891-92); or in H. Reissner, 'Theorie des Erddrucks'. In Encyklopädie der mathematischen Wissenschaften, vol. 4, part 4 (1909), pp. 386-417.
65. Sylvester's paper is not mentioned in the fine survey in F.W.F. Kötter, 'Die Entwicklung der Lehre vom Erddruck'. Jahresbericht der Deutschen Mathematiker-Vereinigung 2, 77-154 (1891-92); or in H. Reissner, 'Theorie des Erddrucks'. In Encyklopädie der mathematischen Wissenschaften, vol. 4, part 4 (1909), pp. 386-417.
66. J.J. Sylvester, 'On Lambert's theorem for elliptic motion', Monthly Notices of the Royal Astronomical Society 26, 27-29 (1865); 'Astronomical prolusions...', Phil. Mag. (4)31, 52-76 (1866). Together in CMP, vol. 2, 496-497, 519-541.
67. J.J. Sylvester, 'On Lambert's theorem for elliptic motion', Monthly Notices of the Royal Astronomical Society 26, 27-29 (1865); 'Astronomical prolusions...', Phil. Mag. (4)31, 52-76 (1866). Together in CMP, vol. 2, 496-497, 519-541.
68. J.J. Sylvester, 'On Lambert's theorem for elliptic motion', Monthly Notices of the Royal Astronomical Society 26, 27-29 (1865); 'Astronomical prolusions...', Phil. Mag. (4)31, 52-76 (1866). Together in CMP, vol. 2, 496-497, 519-541.
69. J.J. Sylvester, 'Note on the periodical changes of orbit...' and 'Supplemental note on the analogues in space to the Cartesian ovals in plano', Phil. Mag. (4)32, 287-300 and 380-385 (1866); also in CMP, vol. 2, 547-563.
70. J.J. Sylvester, 'Note on the periodical changes of orbit...' and 'Supplemental note on the analogues in space to the Cartesian ovals in plano', Phil. Mag. (4)32, 287-300 and 380-385 (1866); also in CMP, vol. 2, 547-563.
71. J.J. Sylvester, Nugae mathematicae (London, 1866).
72. L. Poinsot, Théorie nouvelle de la rotation des corps... (Paris, Bachelier, 1834); English translation, Outline of the theory of rotatory motion (Cambridge, Newby, 1834). For the context of this work, see Grattan-Guinness, op. cit., note 4, pp. 1233-1236. Praising referees' reports by Cayley and W.F. Donkin are conserved in The Royal Society's Archives, RR. 6, 274-275.
73. L. Poinsot, Théorie nouvelle de la rotation des corps... (Paris, Bachelier, 1834); English translation, Outline of the theory of rotatory motion (Cambridge, Newby, 1834). For the context of this work, see Grattan-Guinness, op. cit., note 4, pp. 1233-1236. Praising referees' reports by Cayley and W.F. Donkin are conserved in The Royal Society's Archives, RR. 6, 274-275.
74. L. Poinsot, Théorie nouvelle de la rotation des corps... (Paris, Bachelier, 1834); English translation, Outline of the theory of rotatory motion (Cambridge, Newby, 1834). For the context of this work, see Grattan-Guinness, op. cit., note 4, pp. 1233-1236. Praising referees' reports by Cayley and W.F. Donkin are conserved in The Royal Society's Archives, RR. 6, 274-275.
75. L. Poinsot, Théorie nouvelle de la rotation des corps... (Paris, Bachelier, 1834); English translation, Outline of the theory of rotatory motion (Cambridge, Newby, 1834). For the context of this work, see Grattan-Guinness, op. cit., note 4, pp. 1233-1236. Praising referees' reports by Cayley and W.F. Donkin are conserved in The Royal Society's Archives, RR. 6, 274-275.
76. J.J. Sylvester, 'On the motion of a rigid body acted on by no external forces', Phil. Trans. R. Soc. Lond. 166, 757-780 (1866); summary in Proc. R. Soc. Lond. 15, 139-144 (1866). Together in CMP, vol. 2, pp. 577-607.
77. J.J. Sylvester, 'On the motion of a rigid body acted on by no external forces', Phil. Trans. R. Soc. Lond. 166, 757-780 (1866); summary in Proc. R. Soc. Lond. 15, 139-144 (1866). Together in CMP, vol. 2, pp. 577-607.
78. J.J. Sylvester, 'On the motion of a rigid body acted on by no external forces', Phil. Trans. R. Soc. Lond. 166, 757-780 (1866); summary in Proc. R. Soc. Lond. 15, 139-144 (1866). Together in CMP, vol. 2, pp. 577-607.
79. J.J. Sylvester, 'On an addition to Poinsot's ellipsoidal mode of representing the motion of a rigid body turning freely about a fixed point...', Proc. Lond. Math. Soc. 1 (1866); also in CMP, vol. 2, pp. 517-518.
80. J.J. Sylvester, 'On an addition to Poinsot's ellipsoidal mode of representing the motion of a rigid body turning freely about a fixed point...', Proc. Lond. Math. Soc. 1 (1866); also in CMP, vol. 2, pp. 517-518.
81. See A.C. Rice, R.J. Wilson and J.H. Gardner, 'From student club to national society: the founding of the London Mathematical Society', Historia Mathematica 22, 402-421 (1995); and Rice and Wilson, 'From national to international society: the London Mathematical Society 1867-1900', Historia Mathematica 25, 185-217 (1998).
82. See A.C. Rice, R.J. Wilson and J.H. Gardner, 'From student club to national society: the founding of the London Mathematical Society', Historia Mathematica 22, 402-421 (1995); and Rice and Wilson, 'From national to international society: the London Mathematical Society 1867-1900', Historia Mathematica 25, 185-217 (1998).
83. J.J. Sylvester, Three letters, Nature 1, 482, 532, 582 (1870); also in CMP, vol. 3, pp. 1-6.
84. J.J. Sylvester, Three letters, Nature 1, 482, 532, 582 (1870); also in CMP, vol. 3, pp. 1-6.
85. 'Lettre de M. Peaucellier, capitaine du génie (à Nice)'. Nouvelle Annales des Mathématiques (2)3, 414-415 (1864).
86. J.J. Sylvester, 'On recent discoveries in mechanical conversion of motion', Proc. R. Inst. 7, 179-198 (1873-75); also in Van Nostrand's Mechanical Mag. 12, 313-321 (1875); also in CMP, vol. 3, pp. 7-25. French translation in Revue Scientifique 7, 490-498 (1874). The rambling footnotes contain nice (auto)biographical information.
87. J.J. Sylvester, 'On recent discoveries in mechanical conversion of motion', Proc. R. Inst. 7, 179-198 (1873-75); also in Van Nostrand's Mechanical Mag. 12, 313-321 (1875); also in CMP, vol. 3, pp. 7-25. French translation in Revue Scientifique 7, 490-498 (1874). The rambling footnotes contain nice (auto)biographical information.
88. J.J. Sylvester, 'On recent discoveries in mechanical conversion of motion', Proc. R. Inst. 7, 179-198 (1873-75); also in Van Nostrand's Mechanical Mag. 12, 313-321 (1875); also in CMP, vol. 3, pp. 7-25. French translation in Revue Scientifique 7, 490-498 (1874). The rambling footnotes contain nice (auto)biographical information.
89. J.J. Sylvester, 'On recent discoveries in mechanical conversion of motion', Proc. R. Inst. 7, 179-198 (1873-75); also in Van Nostrand's Mechanical Mag. 12, 313-321 (1875); also in CMP, vol. 3, pp. 7-25. French translation in Revue Scientifique 7, 490-498 (1874). The rambling footnotes contain nice (auto)biographical information.
90. See especially A.B. Kempe, 'On a general method of producing exact rectilinear motion by linkwork', Proc. R. Soc. Lond. 23, 565-577 (1875); French translation in Nouvelle Correspondance Mathématique (3)3 (1877). On this history, involving slightly earlier work by Roberts and several other figures, see T. Koetsier, 'A contribution to the history of kinematics', Mechanism and Machine Theory 18, 37-48 (1983).
91. See especially A.B. Kempe, 'On a general method of producing exact rectilinear motion by linkwork', Proc. R. Soc. Lond. 23, 565-577 (1875); French translation in Nouvelle Correspondance Mathématique (3)3 (1877). On this history, involving slightly earlier work by Roberts and several other figures, see T. Koetsier, 'A contribution to the history of kinematics', Mechanism and Machine Theory 18, 37-48 (1983).
92. See especially A.B. Kempe, 'On a general method of producing exact rectilinear motion by linkwork', Proc. R. Soc. Lond. 23, 565-577 (1875); French translation in Nouvelle Correspondance Mathématique (3)3 (1877). On this history, involving slightly earlier work by Roberts and several other figures, see T. Koetsier, 'A contribution to the history of kinematics', Mechanism and Machine Theory 18, 37-48 (1983).
93. J.J. Sylvester, 'On the plagiograph' and 'History of the plagiograph', Nature 12, 168, 214-216 (1875); also in CMP, vol. 3, pp. 26-34.
94. J.J. Sylvester, 'On the plagiograph' and 'History of the plagiograph', Nature 12, 168, 214-216 (1875); also in CMP, vol. 3, pp. 26-34.
95. J.J. Sylvester, 'On a lady's fan...', Proc. Lond. Math. Soc. 6, 196-197 (1875); also in CMP, vol. 3, pp. 35-36.
96. J.J. Sylvester, 'On a lady's fan...', Proc. Lond. Math. Soc. 6, 196-197 (1875); also in CMP, vol. 3, pp. 35-36.
97. I have not considered Sylvester's many problems posed in Mathematical questions from the Educational Times from 1864 to 1899; a list is given in CMP, vol. 4, pp. 734-739. The ones familiar to me are pure in the sense of this paper, but maybe some applied ones occurred also. Some of his correspondence with the editor, W.J.C. Miller, is printed in Archibald, op. cit., note 3, pp. 124-132, 148-149.
98. I have not considered Sylvester's many problems posed in Mathematical questions from the Educational Times from 1864 to 1899; a list is given in CMP, vol. 4, pp. 734-739. The ones familiar to me are pure in the sense of this paper, but maybe some applied ones occurred also. Some of his correspondence with the editor, W.J.C. Miller, is printed in Archibald, op. cit., note 3, pp. 124-132, 148-149.
99. I have not considered Sylvester's many problems posed in Mathematical questions from the Educational Times from 1864 to 1899; a list is given in CMP, vol. 4, pp. 734-739. The ones familiar to me are pure in the sense of this paper, but maybe some applied ones occurred also. Some of his correspondence with the editor, W.J.C. Miller, is printed in Archibald, op. cit., note 3, pp. 124-132, 148-149.
100. See K.H. Parshall and D. Rowe, The emergence of the American mathematical research community (Providence, Rhode Island, American Mathematical Society, 1994), esp. ch. 2 and 3.
101. J.J. Sylvester, 'The algebraical theory of the secular-inequality determinative equation generalized' and 'On the explicit values of Sturm's quotients', Phil. Mag. (5)6, 214-216 and 293-296 (1853); together in CMP, vol. 1, pp. 634-640. On the prehistory of this problem see T.W. Hawkins, 'Cauchy and the spectral theory of matrices', Historia Mathematica 2, 1-29 (1975); on Sylvester's work on the separation and reality of roots, see H. Sinaceur, Corps et modèles (Paris, Vrin, 1991), esp. pp. 124-140.
102. J.J. Sylvester, 'The algebraical theory of the secular-inequality determinative equation generalized' and 'On the explicit values of Sturm's quotients', Phil. Mag. (5)6, 214-216 and 293-296 (1853); together in CMP, vol. 1, pp. 634-640. On the prehistory of this problem see T.W. Hawkins, 'Cauchy and the spectral theory of matrices', Historia Mathematica 2, 1-29 (1975); on Sylvester's work on the separation and reality of roots, see H. Sinaceur, Corps et modèles (Paris, Vrin, 1991), esp. pp. 124-140.
103. J.J. Sylvester, 'The algebraical theory of the secular-inequality determinative equation generalized' and 'On the explicit values of Sturm's quotients', Phil. Mag. (5)6, 214-216 and 293-296 (1853); together in CMP, vol. 1, pp. 634-640. On the prehistory of this problem see T.W. Hawkins, 'Cauchy and the spectral theory of matrices', Historia Mathematica 2, 1-29 (1975); on Sylvester's work on the separation and reality of roots, see H. Sinaceur, Corps et modèles (Paris, Vrin, 1991), esp. pp. 124-140.
104. J.J. Sylvester, 'The algebraical theory of the secular-inequality determinative equation generalized' and 'On the explicit values of Sturm's quotients', Phil. Mag. (5)6, 214-216 and 293-296 (1853); together in CMP, vol. 1, pp. 634-640. On the prehistory of this problem see T.W. Hawkins, 'Cauchy and the spectral theory of matrices', Historia Mathematica 2, 1-29 (1975); on Sylvester's work on the separation and reality of roots, see H. Sinaceur, Corps et modèles (Paris, Vrin, 1991), esp. pp. 124-140.
105. J.J. Sylvester, 'On the equation to the secular inequalities in the planetary theory', Phil. Mag. (5)16, 267-269 (1883); also in CMP, vol. 4, pp. 110-111.
106. J.J. Sylvester, 'On the equation to the secular inequalities in the planetary theory', Phil. Mag. (5)16, 267-269 (1883); also in CMP, vol. 4, pp. 110-111.
107. J.J. Sylvester, 'Presidential address'. Reports of the British Association for the Advancement of Science (1869; published 1870), pp. 1-9; also in CMP, vol. 2, 650-661; also in W.B. Ewald (ed.), From Kant to Hilbert. A source book in the foundations of mathematics, 2 vols (New York and Oxford, Clarendon Press, 1996), pp. 511-522. The address, which was designed as a reply to a ridiculous dismissal of mathematics by T.H. Huxley, led to an extensive discussion of Kant's philosophy; it is reprinted in CMP, vol. 2, pp. 714-731.
108. J.J. Sylvester, 'Presidential address'. Reports of the British Association for the Advancement of Science (1869; published 1870), pp. 1-9; also in CMP, vol. 2, 650-661; also in W.B. Ewald (ed.), From Kant to Hilbert. A source book in the foundations of mathematics, 2 vols (New York and Oxford, Clarendon Press, 1996), pp. 511-522. The address, which was designed as a reply to a ridiculous dismissal of mathematics by T.H. Huxley, led to an extensive discussion of Kant's philosophy; it is reprinted in CMP, vol. 2, pp. 714-731.
109. J.J. Sylvester, 'Presidential address'. Reports of the British Association for the Advancement of Science (1869; published 1870), pp. 1-9; also in CMP, vol. 2, 650-661; also in W.B. Ewald (ed.), From Kant to Hilbert. A source book in the foundations of mathematics, 2 vols (New York and Oxford, Clarendon Press, 1996), pp. 511-522. The address, which was designed as a reply to a ridiculous dismissal of mathematics by T.H. Huxley, led to an extensive discussion of Kant's philosophy; it is reprinted in CMP, vol. 2, pp. 714-731.
110. J.J. Sylvester, 'Presidential address'. Reports of the British Association for the Advancement of Science (1869; published 1870), pp. 1-9; also in CMP, vol. 2, 650-661; also in W.B. Ewald (ed.), From Kant to Hilbert. A source book in the foundations of mathematics, 2 vols (New York and Oxford, Clarendon Press, 1996), pp. 511-522. The address, which was designed as a reply to a ridiculous dismissal of mathematics by T.H. Huxley, led to an extensive discussion of Kant's philosophy; it is reprinted in CMP, vol. 2, pp. 714-731.
111. Some features will be made manifest in Parshall and Rice, op. cit., note 6. The special case of Germany is well handled in G. Schubring, Die Entstehung des Mathematiklehrerberufs im 19. Jahrhundert. Studien und Materialien zum Prozeß der Professionalisierung in Preuβen (1810-1870), 2nd edn (Weinheim, Deutscher Studien Verlag, 1991).
112. Some features will be made manifest in Parshall and Rice, op. cit., note 6. The special case of Germany is well handled in G. Schubring, Die Entstehung des Mathematiklehrerberufs im 19. Jahrhundert. Studien und Materialien zum Prozeß der Professionalisierung in Preuβen (1810-1870), 2nd edn (Weinheim, Deutscher Studien Verlag, 1991).