Calculus and Analysis in Early 19th-Century Britain: The Work of William Wallace

Historia Mathematica

Volumn 26, Issue 3, 1999, Pages 239-267

  Craik, Alex D D ^a,b  

^a UNIVERSITY OF ST ANDREWS   (United Kingdom)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037553605     PISSN: 03150860     EISSN: None     Source Type: Journal    
DOI: 10.1006/hmat.1999.2250     Document Type: Article

References (106)

1. Edinburgh University Library: Papers relating to William Wallace, Dc.4.101.
2. British Library, London, Macvey Napier Correspondence: Add. MSS. 34,611, William Wallace to MN: (a) f. 189, 3 April 1815; (b) f. 286, 28 Sept. 1815. J. Ivory to MN: (c) f. 334, 5 Feb. 1816; (d) f. 324, 10 Jan. 1817; (e) f. 439, 29 August 1817; (f) f. 308, Nov. 1819. R Woodhouse to MN: (g) f. 63, 22 May 1814. Add. MSS. 34,612, Thomas Young to MN: (h) f. 35, 22 Feb. 1817.
3. British Library, London, Charles Babbage Correspondence: Add. MSS. 37,182, James Ivory to CB: (a) f. 36, 6 Nov. 1815; (b) f. 50, 21 Feb. 1816; (c) ff. 62-70, Mar./April 1816; (d) ff. 127-129, July 1819; (e) ff. 149-158, printed testimonials 1819. Edward F. Bromhead to CB: (f) ff. 13-14, n.d. [1813?].
4. Royal Society of London, Correspondence of Sir John F. W. Herschel: William Wallace to JH: (a) HS.18.21, 31 July 1815; (b) HS.18.22, 29 Oct. 1817; (c) HS.18.27, 21 Oct. 1840. JH to William Wallace: (d) HS.20.25, 23 Sept. 1815; (e) HS.20.226, Dec. 12 1825 (copybook). JH to Charles Babbage: (f) HS.20.38, 30 Jan. 1817 (copybook). JH to David Brewster: (g) HS.20.175, 27 Nov. 1824 (copybook).
5. University College London, Brougham Papers: David Brewster to Henry Brougham: (a) 26,612, 17 Oct. 1831. James Ivory to HB: (b) 8,614, 22 Oct. 1831; (c) 37,678, 10 Jan. 1832. John Leslie to HB: (d) 16,442, 11 Sept. 1831. William Wallace to HB: (e) 27,385, 10 July 1822; (f) 37,952, 15 April 1832; (g) 34,879, 8 Aug. 1832; (h) 27,711, 19 May 1835; (i) 27,956, 22 May 1839.
6. Alexander Aitchison, ed., Encyclopaedia Perthensis or Universal Dictionary of Knowledge Collected from Every Source and Intended to Supersede the Use of All Other English Books of Reference ... in Twenty-Three Volumes, Perth: W. Morison (1796-1806); also C. Mitchell & Co. (n.d.).
7. Adrien-Marie Ampère, Recherches sur quelques points de la théorie des fonctions dérivées ..., Journal de l'École polytechnique (1) 6, No. 13, 148-181.
8. Anon., Obituary of Sir James Ivory, Abstracts of the Papers Printed in the Philosophical Transactions of the Royal Society of London 4 (1837-1843), 406-412 . Other biographies are in James Fullarton, The Scottish Nation, 1869, 548-550; A Biographical Dictionary of Eminent Scotsmen, 3 vols., Glasgow, Edinburgh & London: Blackie & Son (1869-1872), 2:351-352; William Norrie, Dundee Celebrities of the Nineteenth Century ..., Dundee: W. Norrie, 1873, 70-73; Margaret E. Baron, Dictionary of Scientific Biography, 16 vols., 2 supps., ed. Charles C. Gillispie, New York: Charles Scribner's Sons, 1970-1990, 7:37.
9. Anon., Obituary of Sir James Ivory, Abstracts of the Papers Printed in the Philosophical Transactions of the Royal Society of London 4 (1837-1843), 406-412 . Other biographies are in James Fullarton, The Scottish Nation, 1869, 548-550; A Biographical Dictionary of Eminent Scotsmen, 3 vols., Glasgow, Edinburgh & London: Blackie & Son (1869-1872), 2:351-352; William Norrie, Dundee Celebrities of the Nineteenth Century ..., Dundee: W. Norrie, 1873, 70-73; Margaret E. Baron, Dictionary of Scientific Biography, 16 vols., 2 supps., ed. Charles C. Gillispie, New York: Charles Scribner's Sons, 1970-1990, 7:37.
10. Anon., Obituary of Sir James Ivory, Abstracts of the Papers Printed in the Philosophical Transactions of the Royal Society of London 4 (1837-1843), 406-412 . Other biographies are in James Fullarton, The Scottish Nation, 1869, 548-550; A Biographical Dictionary of Eminent Scotsmen, 3 vols., Glasgow, Edinburgh & London: Blackie & Son (1869-1872), 2:351-352; William Norrie, Dundee Celebrities of the Nineteenth Century ..., Dundee: W. Norrie, 1873, 70-73; Margaret E. Baron, Dictionary of Scientific Biography, 16 vols., 2 supps., ed. Charles C. Gillispie, New York: Charles Scribner's Sons, 1970-1990, 7:37.
11. Anon., Obituary of Sir James Ivory, Abstracts of the Papers Printed in the Philosophical Transactions of the Royal Society of London 4 (1837-1843), 406-412 . Other biographies are in James Fullarton, The Scottish Nation, 1869, 548-550; A Biographical Dictionary of Eminent Scotsmen, 3 vols., Glasgow, Edinburgh & London: Blackie & Son (1869-1872), 2:351-352; William Norrie, Dundee Celebrities of the Nineteenth Century ..., Dundee: W. Norrie, 1873, 70-73; Margaret E. Baron, Dictionary of Scientific Biography, 16 vols., 2 supps., ed. Charles C. Gillispie, New York: Charles Scribner's Sons, 1970-1990, 7:37.
12. Anon., Obituary of Sir James Ivory, Abstracts of the Papers Printed in the Philosophical Transactions of the Royal Society of London 4 (1837-1843), 406-412 . Other biographies are in James Fullarton, The Scottish Nation, 1869, 548-550; A Biographical Dictionary of Eminent Scotsmen, 3 vols., Glasgow, Edinburgh & London: Blackie & Son (1869-1872), 2:351-352; William Norrie, Dundee Celebrities of the Nineteenth Century ..., Dundee: W. Norrie, 1873, 70-73; Margaret E. Baron, Dictionary of Scientific Biography, 16 vols., 2 supps., ed. Charles C. Gillispie, New York: Charles Scribner's Sons, 1970-1990, 7:37.
13. Anon., Obituary of William Wallace, Monthly Notices of the Royal Astronomical Society 6 (1845), 31-41.
14. Louis-F.-A. Arbogast, Du calcul des dérivations, Strasbourg: de Levrault, 1800.
15. Charles Babbage, An Essay towards the Calculus of Functions, Philosophical Transactions of the Royal Society of London 105 (1815), 389-423; 106 (1816), 179-256.
16. Charles Babbage, An Essay towards the Calculus of Functions, Philosophical Transactions of the Royal Society of London 105 (1815), 389-423; 106 (1816), 179-256.
17. Charles Babbage, Reflections on the Decline of Science in England and on Some of Its Causes, London: B. Fellows, 1830.
18. Harvey W. Becher, Woodhouse, Babbage, Peacock, and Modern Algebra, Historia Mathematica 7 (1980), 389-400.
19. Harvey W. Becher, William Whewell and Cambridge Mathematics, Historical Studies in the Physical Sciences 11 (1980), 1-48.
20. Harvey W. Becher, Radicals, Whigs and Conservatives: The Middle and Lower Classes in the Analytical Revolution at Cambridge in the Age of Aristocracy, British Journal for the History of Science 28 (1995), 405-426.
21. Umberto Bottazzini, The Higher Calculus: A History of Real and Complex Analysis from Euler to Weierstrass, New York: Springer-Verlag, 1986.
22. Charles B. Boyer, A History of Mathematics, Princeton, NJ: Princeton Univ. Press, 1968.
23. David Brewster, ed., The Edinburgh Encyclopaedia, 18 vols., Edinburgh: Blackwood, 1808-1830.
24. [David Brewster], (a) Decline of Science in England and Patent Laws, Quarterly Review 43 (1830), 305-342;
25. (b) Observations on the Decline of Science in England, Edinburgh Journal of Science, New Ser. 5 (1831), 1-16;
26. (c) Observations on a Pamphlet Entitled On the Alleged Decline of Science in England, by a Foreigner, Edinburgh Journal of Science, New Ser. 5 (1831), 334-358.
27. [David Brewster], Review of William Whewell's History of the Inductive Sciences, Edinburgh Review 66 (1837-1838), 110-151.
28. T. A. A. Broadbent, William Wallace, in Dictionary of Scientific Biography, ed. Charles C. Gillispie, 16 vols., 2 supp., New York: Charles Scribner's Sons, 1973, 14:140-141.
29. William H. Brock, Brewster as a Scientific Journalist, in "Martyr of Science": Sir David Brewster 1781-1868, ed. A. D. Morrison-Low & J. R. R. Christie, Edinburgh: Royal Scottish Museum Studies, 1984, pp. 36-42.
30. Stephen G. Brush, John Herapath, Dictionary of Scientific Biography, ed. Charles C. Gillispie, 16 vols., 2 supps., New York: Charles Scribner's Sons, 1973, 6:291-293.
31. Anand C. Chitnis, The Scottish Enlightenment & Early Victorian English Society, London: Croom Helm, 1986.
32. I. Bernard Cohen, Preface to The Works of Charles Babbage, 11 vols., ed. Martin Campbell-Kelly, London: Wm. Pickering, 1989, 1:16.
33. Alex D. D. Craik, Geometry, Analysis and the Baptism of Slaves: John West in Scotland and Jamaica, Historia Mathematica 25 (1998), 29-74.
34. George E. Davie, The Democratic Intellect, Edinburgh: Edinburgh Univ. Press, 1961.
35. John M. Dubbey, The Mathematical Work of Charles Babbage, Cambridge, UK: Cambridge Univ. Press, 1978.
36. Charles H. Edwards, The Historical Development of the Calculus, New York: Springer-Verlag, 1979.
37. Paul C. Enros, The Analytical Society (1812-1813): Precursor of the Renewal of Cambridge Mathematics, Historia Mathematica 10 (1983), 14-47.
38. James D. Forbes, Dissertation Sixth: Exhibiting a General View of the Progress of Mathematical and Physical Science ... Particularly between 1775 and 1850, Encyclopaedia Britannica, 8th ed., Edinburgh: Adam & Charles Black, 1857, 1:795-996. [Later published separately]
39. Judith V. Grabiner, The Origins of Cauchy's Rigorous Calculus, Cambridge, MA.: MIT Press, 1981.
40. Judith V. Grabiner, Was Newton's Calculus a Dead End? The Continental Influence of Maclaurin's Treatise of Fluxions, American Mathematical Monthly 104 (1997), 393-410.
41. Ivor Grattan-Guinness, Babbage's Mathematics in Its Time, British Journal for the History of Science 12 (1979), 82-88.
42. Ivor Grattan-Guinness, Mathematical Research and Instruction in Ireland: 1782-1840, in Science in Ireland 1800-1930: Tradition and Reform, ed. John R. Nudds, Norman D. McMillan, Denis L. Weaire, and Susan M. P. McKenna Lawlor, Dublin: Trinity College, 1988.
43. Ivor Grattan-Guinness, Convolutions in French Mathematics, 1800-1840, 3 vols., Basel: Birkhäuser, 1990.
44. Ivor Grattan-Guinness, The Young Mathematician, in John Herschel 1792-1871: A Bicentennial Commemoration, ed. David G. King-Hele, London: The Royal Society, 1992, pp. 17-28.
45. Duncan F. Gregory, Examples of the Processes of the Differential and Integral Calculus, 1st ed. 1841; 2nd ed. (ed. W. Walton) Cambridge, UK: J. & J. J. Deighton, 1846.
46. Niccolò Guicciardini, The Development of Newtonian Calculus in Britain 1700-1800, Cambridge, UK: Cambridge Univ. Press, 1989.
47. Marie Boas Hall, All Scientists Now: The Royal Society in the Nineteenth Century, Cambridge, UK: Cambridge Univ. Press, 1984.
48. Peter M. Harman, ed., Wranglers and Physicists, Manchester: Manchester Univ. Press, 1985.
49. John F. W. Herschel, Mathematics, in Edinburgh Encyclopaedia, ed. D. Brewster, 18 vols., Edinburgh: Blackwood, 1808-1830.
50. Charles Hutton, ed., A Mathematical and Philosophical Dictionary ..., 2 vols., London: J. Davies for J. Johnson, J. Robinson, 1795; new ed. with additions, as A Philosophical and Mathematical Dictionary ..., 1815.
51. Charles Hutton, ed., A Mathematical and Philosophical Dictionary ..., 2 vols., London: J. Davies for J. Johnson, J. Robinson, 1795; new ed. with additions, as A Philosophical and Mathematical Dictionary ..., 1815.
52. James Ivory, Equations, in Supplement to the 4th, 5th and 6th eds. of the Encyclopaedia Britannica, ed. Macvey Napier, 6 vols., Edinburgh: A. Constable, 1824.
53. James Ivory, On the Theory of the Figure of the Planets Contained in the Third Book of the Mécanique Céleste, Philosophical Magazine & Journal 67 (1826), 31-37, 81-86.
54. Silvestre F. Lacroix, Traité du calcul différentiel et du calcul intégral, 3 vols., Paris: Duprat, 1797-1800; 2nd ed., 1810-1815.
55. Silvestre F. Lacroix, Traité élémentaire du calcul différentiel et du calcul intégral, Paris: Duprat, 1802.
56. Silvestre F. Lacroix, An Elementary Treatise of the Differential and Integral Calculus, trans. Charles Babbage, John Herschel, and George Peacock, Cambridge, UK: J. Deighton, 1816.
57. Joseph-Louis Lagrange, Théorie des fonctions analytiques, Paris: Imprimerie impériale, 1797; 2d ed., 1813 in Oeuvres de Lagrange, ed. Joseph A. Serret and Gaston Darboux, 14 vols., Paris, Gauthier-Villars 1867-1892, vol. 9.
58. Joseph-Louis Lagrange, Théorie des fonctions analytiques, Paris: Imprimerie impériale, 1797; 2d ed., 1813 in Oeuvres de Lagrange, ed. Joseph A. Serret and Gaston Darboux, 14 vols., Paris, Gauthier-Villars 1867-1892, vol. 9.
59. Pierre-Simon de Laplace, Treatise upon Analytical Mechanics; Being the First Book of the Méchanique Céleste of P. S. Laplace, trans. John Toplis, Nottingham: H. Barnett, 1814.
60. Adrien-Marie Legendre, Mémoire sur les transcendantes elliptiques, Mémoires de l'Académie royale des sciences (1794), 1-102.
61. John Leslie, Elements of Geometry, Geometrical Analysis and Plane Trigonometry, Edinburgh: J. Ballantyne, 1809; later eds., 1811, 1817, 1820.
62. John Leslie, Dissertation Fourth on the Progress of Mathematical and Physical Sciences Chiefly during the Eighteenth Century, in Encyclopaedia Britannica, 7th ed., 1842. Also in Dugald Stewart, John Leslie, et al., Treatises on Various Subjects of Natural and Chemical Philosophy, Edinburgh: A. & C. Black, 1838, pp. 575-677.
63. John Leslie, Dissertation Fourth on the Progress of Mathematical and Physical Sciences Chiefly during the Eighteenth Century, in Encyclopaedia Britannica, 7th ed., 1842. Also in Dugald Stewart, John Leslie, et al., Treatises on Various Subjects of Natural and Chemical Philosophy, Edinburgh: A. & C. Black, 1838, pp. 575-677.
64. Alexander Macfarlane, Lectures on Ten British Mathematicians of the Nineteenth Century, New York & London: Wiley, Chapman-Hall, 1916.
65. Thomas Miller, A Treatise on the Differential Calculus; With Its Application to Plane Curves, to Curve Lines, and to Curves of Double Curvature, Edinburgh: Maclachlan & Stewart, 1854.
66. Carlisle Moore, Carlyle, Mathematics and "Mathesis," in Carlyle Past and Present, ed. K. J. Fielding and R. L. Tarr, New York: Barnes & Noble, 1976, pp. 61-95.
67. Jack B. Morrell, Science and Scottish University Reform: Edinburgh in 1826, British Journal for the History of Science 6 (1972), 39-56.
68. Jack B. Morrell and Arnold Thackray, Gentlemen of Science: Early Years of the British Association for the Advancement of Science, London: Royal History Society, 1981.
69. Richard Olson, Scottish Philosophy and British Physics, 1750-1880, Princeton, NJ: Princeton University Press, 1975.
70. Maria Panteki, William Wallace and the Introduction of Continental Calculus to Britain: A Letter to George Peacock, Historia Mathematica 14 (1987), 119-132.
71. George Peacock, Report on Certain Branches of Analysis, Report of the British Association for the Advancement of Science for 1833, Cambridge, BAAS: 1833, pp. 185-352.
72. Abraham Rees, ed., The Cyclopaedia, or Universal Dictionary of Arts, Sciences & Literature, 39 vols., London: Longman, Hurst, Rees etc., 1802-1819.
73. Adrian Rice, Inspiration or Desperation? Augustus De Morgan's Appointment to the Chair of Mathematics at London University in 1828, British Journal for the History of Science 30 (1997), 257-274.
74. Alonso D. Roberts, St. Andrews University Mathematics Teaching, 1765-1858, unpublished M.Ed, thesis, University of Dundee, 1970.
75. William Rouse Ball, A History of the Study of Mathematics at Cambridge, Cambridge, UK: Cambridge Univ. Press, 1889.
76. William Rouse Ball, A Short Account of the History of Mathematics, 4th ed., London: Macmillan, 1908.
77. Charles R. Sanders, Kenneth J. Fielding, et al., ed. The Collected Letters of Thomas and Jane Welsh Carlyle, Duke-Edinburgh edition, 25 vols., Durham, NC: Duke University Press, 1970.
78. John F. Scott, A History of Mathematics, London: Taylor & Francis, 1960.
79. William Spence, An Essay on the Theory of the Various Orders of Logarithmic Transcendents; With an Inquiry into Their Applications to the Integral Calculus and the Summation of Series, London: John Murray, Edinburgh: Arch. Constable & Co., 1809.
80. William Spence, Mathematical Essays, by the Late William Spence, Esq. Edited by John F. W. Herschel, Esq. with a Brief Memoir of the Author, London: J. Moyes for Oliver and Boyd, G. & W. B. Whittaker, 1820.
81. George Stronach, William Wallace, Dictionary of National Biography 20 (1899), 572-573.
82. John Thompson, The Madras College, 1833-1983, 150th Anniversary Publication, St Andrews: privately published, 1984.
83. Isaac Todhunter, A History of the Mathematical Theories of Attraction and the Figure of the Earth, 2 vols., London: Macmillan 1873; 2 vols, in 1, New York: Dover, 1962.
84. John Toplis, On the Decline of Mathematical Studies, and the Sciences Dependent upon Them, Philosophical Magazine 20 (1805), 25-31.
85. William Wallace, New Series for the Quadrature of the Conic Sections, and the Computation of Logarithms, Transactions of the Royal Society of Edinburgh 6 (1812), 269-344.
86. William Wallace, Fluxions, in Encyclopaedia Britannica, 4th ed., Edinburgh: A. Bell, 1810, 8:697-778.
87. William Wallace, Fluxions, in The Edinburgh Encyclopaedia, ed. D. Brewster, 18 vols., Edinburgh: Blackwood, 1808-1830, 9:382-467.
88. [William Wallace], Elements of Plane Trigonometry with Their Application to Mensuration and Surveying, Edinburgh: n.p., 1820.
89. William Wallace, Fluxions, in Encyclopaedia Britannica, 7th ed., Edinburgh: A. & C. Black, 1842, 7:218-262.
90. [William Wallace], Euclid's Elements of Geometry, 7th ed., ed. John Playfair, with additions by William Wallace, Edinburgh: Bell & Bradfute, 1826.
91. [William Wallace] "G.V.", (a) Analytical Investigation of a Formula which Shall Express the Relative Importance of a Certain Number of the Boroughs in England and Wales, Philosophical Magazine, new ser. 11 (1832), 218-223;
92. (b) Addition to the Analytical Investigation ... and a Reply to Dr. M'Intyre's Remarks, 3rd ser. 1 (1832), 26-31;
93. Dr. M'Intyre's paper is (c) Philosophical Magazine, new ser. 11 (1832), 360-362.
94. William Wallace, A Geometrical Treatise on the Conic Sections with an Appendix Containing Formulae for their Quadrature, Edinburgh: A. & C. Black, 1838.
95. William Wallace, Geometrical Theorems and Analytical Formulae with their Application to the Solution of Certain Geodetical Problems and an Appendix, Containing a Description of Two Copying Instruments, Edinburgh: A. & C. Black, 1839.
96. William Wallace, Solution of a Functional Equation, with Its Application to the Parallelogram of Forces, Transactions of the Royal Society of Edinburgh 15 (1840), 431-448.
97. [William Wallace], Testimonials for William Wallace, F.R.S.E. ... as a Candidate for the Mathematical Chair in the University of Edinburgh, Edinburgh: printed pamphlet, September 1819. Copy in J. D. Forbes Collection, University of St Andrews, the first item in "Edinburgh Tracts, vol. XI, Testimonials 1819-1828."
98. [William Wallace], Catalogue of the Valuable Library of the Late William Wallace LL.D. ... Sold at Auction by Messrs C. B. Tait & Co ... Edinburgh: Colston, 1843, 28 pp. Copy in J. D. Forbes Collection, University of St Andrews.
99. John West, Mathematical Treatises, Containing I. The Theory of Analytic Functions. II. Spherical Trigonometry, with Practical and Nautical Astronomy ... Edited (after the Author's Death) from his Mss. by the Late Sir John Leslie ... Accompanied by a Memoir of the Life and Writings of the Author by Edward Sang, F.R.S.E., Edinburgh: Oliver & Boyd/London: Simpkin, Marshall & Co., 1838.
100. William Whewell, History of the Inductive Sciences, from Earliest to the Present Times, 3 vols., London: J. W. Parker etc., 1837.
101. William Whewell, The Doctrine of Limits with Its Applications, Namely, to Conic Sections, the First Three Sections of Newton, the Differential Calculus, Cambridge, UK: J. & J. J. Deighton/London: J. W. Parker, 1838.
102. William Whewell, The Philosophy of the Inductive Sciences, London: J. W. Parker, 1840.
103. Maurice V. Wilkes, Herschel, Peacock, Babbage and the Development of the Cambridge Curriculum, Notes and Records of the Royal Society of London 44 (1990), 205-219.
104. T. W. Wilkinson, On Leybourn's Mathematical Repository, Mechanics' Magazine 55 (1851), 264-266, 306-310, 363-365, 445-448; 56 (1852), 7-9, 64-66, 245-247, 291-294.
105. T. W. Wilkinson, On Leybourn's Mathematical Repository, Mechanics' Magazine 55 (1851), 264-266, 306- 310, 363-365, 445-448; 56 (1852), 7-9, 64-66, 245-247, 291-294.
106. Robert Woodhouse, The Principles of Analytic Calculation, Cambridge, UK: Cambridge Univ. Press, 1803.