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James Lockhart (banker)

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James Lockhart (1763–1852) was an English banker who wrote on numerical analysis.[1]

Life

He was one of three children and two sons of James Lockhart (1735–1814), a Scottish banker, and his wife Mary Harriot Gray or Grey, from a Quaker family; John Ingram Lockhart was his brother, and the daughter was Mary Harriett, married name Greenwollers. He was educated at Reading School and Eton College.[1][2][3][4]

Lockhart worked as a banker in Pall Mall, London, in his father's firm Lockhart, Wallace, & Co. He became a partner, and set up the Cattle Insurance Company.[1][5][6] Retiring from the bank in 1799, he moved north to the Windermere area after the death of his first wife.[1]

Lockhart knew Walking Stewart, and stated he had learned from him. He knew also William Combe, and the idea for Combe's "Dr Syntax" has been attributed to him. He taught mathematics to his own children, and pupils including Joshua King.[1]

For about 15 years Lockhart and his family resided in the Netherlands, from 1819, in Leyden and then Haarlem. He returned to England on the death in 1835 of his brother John, who left no heir.[1]

Living first at Aylesbury, Lockhart moved to the rectory at Cowley in 1837. After a legal case on his brother's will, the estate at Cowley was sold in 1841. He moved to Brompton.[1] In 1847 his address was given as Lanhams, near Braintree, Essex.[7]

Taking a lease on shooting on the Scottish island of Raasay, Lockhart spent time from 1845 on the Isle of Skye. He then lived in an Argyllshire mansion. He moved in 1851 to Clitsome House near Washford in Somerset.[1] He died there the following year.[8]

Works

Lockhart proposed challenge problems on the separation of the roots of equations of degree five and six, some being published in 1841.[9] He was still writing on the theory of equations while in Argyllshire.[10] The challenges were considered by Florian Cajori to have influenced the work of John Radford Young;[11] William Rutherford noted an analysis by Young of an equation proposed by Lockhart, in a book of 1849.[12]

Detailed analysis of a quintic using Budan's theorem for separation of roots was given in 1842, by James R. Christie;[13] it was noted by Young.[14] In 1843 Young commented that Budan's approach, and Lockhart's own ideas, could now be simplified on the basis of recent developments, which had led to Sturm's theorem.[15] Young also commended books by Lockhart in discussing a problem on roots proposed by John Pell to Silius Titus.[16] Lockhart and Young then influenced the subsequent work of Rehuel Lobatto.[17]

Lockhart's books were mostly self-published:

  • A Method of Approximating Towards the Roots of Cubic Equations Belonging to the Irreducible Case (1813)[18]
  • Nieuwe en algemeene leerwijze om biquadraten op te lossen waarbij de systemas van Descartes en Euler tot biquadraten met derzelver tweede termen worden voortgezet (1823)[19]
  • Nieuwe oplossing van cubiek-vergelykingen door juiste uitdrukkingen, en ook bij nadering, zonder beproeving of gissing (1825)[20]
  • Extension of the celebrated theorem of C. Sturm, whereby the roots of numeral equations may be separated from each other, with copious examples (1839)[21]
  • Resolution of Two Equations (1839)[22]
  • Resolution of Equations by Means of Inferior and Superior Limits (1842)[23]
  • The Nature of the Roots of Numerical Equations (1850)[24]

Family

Lockhart married twice. With his first wife, Mary Coxe, daughter of Leonard Coxe of Philadelphia, a dispossessed loyalist of the American Revolution, he had three daughters and a son.[1][25] With his second wife Elizabeth, whom he married in 1805, he had six sons and two daughters; she died in 1843 at age 56.[1][26] Lockhart's children included:

Notes

  1. ^ a b c d e f g h i j Monthly Notices of the Royal Astronomical Society. Priestley and Weale. 1853. pp. 112–.
  2. ^ The Gentleman's Magazine and Historical Review. J.H. and J. Parker. 1866. p. 198.
  3. ^ "Lockhart, John Ingram (1765–1835), of Great Haseley, Oxon., History of Parliament Online". Retrieved 6 April 2016.
  4. ^ "To be premptorily sold". Berkshire Chronicle. 4 October 1851. p. 1. Retrieved 6 April 2016.
  5. ^ Williams, William Retlaw. "The Parliamentary History of the County of Oxford, including the city and university of Oxford, and the boroughs of Banbury, Burford, Chipping Norton, Dadington, Witney, and Woodstock, from the earliest times to the present day, 1213-1899, with biographical and genealogical notices of the members". Internet Archive. Brecknock: Priv. Print. for the author by E. Davies. p. 131. Retrieved 6 April 2016.
  6. ^ A Biographical Dictionary of the Living Authors of Great Britain and Ireland: Comprising Literary Memoirs and Anecdotes of Their Lives, and a Chronological Register of Their Publications, with the Number of Editions Printed; Including Notices of Some Foreign Writers Whose Works Have Been Occasionally Published in England. Henry Colburn. 1816. p. 208.
  7. ^ Memoirs of the Royal Astronomical Society. 1847. p. 573.
  8. ^ The Gentleman's Magazine. W. Pickering. 1852. p. 215.
  9. ^ The Mathematician. G. Bell. 1845. p. 165.
  10. ^ Thomas Stephen Davies; Stephen Fenwick; William Rutheford (1850). The Mathematician. G. Bell. p. 223.
  11. ^ Cajori, Florian (1910). "A History of the Arithmetical Methods of Approximation to the Roots of Numerical Equations of one Unknown Quantity Part III Modern Times". Colorado College. p. 234. Retrieved 6 April 2016.
  12. ^ William Rutherford (1849). The Complete Solution of Numerical Equations: in Which, by One Uniform Process, the Imaginary as Well as the Real Roots are Easily Determined. p. 20.
  13. ^ The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. Taylor & Francis. 1842. p. 99.
  14. ^ J. R. Young (1844). Researches respecting the Imaginary Roots of Numerical Equations. p. 55, note.
  15. ^ John Radford Young (1843). Theory and Solution of Algebraical Equations of the Higher Orders. Souter and Law. p. 245.
  16. ^ John Radford Young (1841). Mathematical Dissertations, for the Use of Students in the Modern Analysis. John Souter. pp. 159–60 and notes.
  17. ^ The Quarterly Journal of Pure and Applied Mathematics. 1862. p. 240.
  18. ^ James Lockhart (1813). A Method of Approximating Towards the Roots of Cubic Equations Belonging to the Irreducible Case.
  19. ^ James Lockhart (1823). Nieuwe en algemeene leerwijze om biquadraten op te lossen waarbij de systemas van Descartes en Euler tot biquadraten met derzelver tweede termen worden voortgezet.
  20. ^ James Lockhart (1825). Nieuwe oplossing van cubiek-vergelykingen door juiste uitdrukkingen, en ook bij nadering, zonder beproeving of gissing. erven François Bohn.
  21. ^ James Lockhart (1839). Extension of the celebrated theorem of C. Sturm, whereby the roots of numeral equations may be separated from each other, with copious examples. the Author. p. 1.
  22. ^ James Lockhart (1839). Resolution of Two Equations. Being a homage to the memory of the founders and benefactors of the University of Oxford, at the Commemoration held on the 12th of June, 1839. the Author.
  23. ^ James Lockhart (1842). Resolution of Equations by Means of Inferior and Superior Limits. Lockhart.
  24. ^ James Lockhart (1850). The Nature of the Roots of Numerical Equations. C. and J. Adlard.
  25. ^ Walford, Edward (1868). "The County Families of the United Kingdom; or, Royal manual of the titled and untitled aristocracy of England, Wales, Scotland, and Ireland ." Internet Archive. London: R. Hardwicke. p. 593. Retrieved 6 April 2016.
  26. ^ The Gentleman's Magazine. F. Jefferies. 1843. p. 104.
  27. ^ s:Page:Men-at-the-Bar.djvu/319
  28. ^ Catherine Reilly (2000). Mid-Victorian Poetry, 1860-1879. A&C Black. p. 280. ISBN 978-0-7201-2318-0.
  29. ^ Henry Press Wright (1873). The Story of the "Domus Dei" of Portsmouth, Commonly Called The Royal Garrison Church. J. Parker. p. 78.
  30. ^ "The Late Captain Lockhart". Hampshire Chronicle. 27 October 1855. p. 5. Retrieved 6 April 2016.
  31. ^ "Nicolaas Beets, Het dagboek van de student Nicolaas Beets, 1833-1836 · dbnl" (in Dutch). Retrieved 6 April 2016.
  32. ^ Stewart, John H. J. (1880). "Stewarts of Appin". Internet Archive. Edinburgh: Maclachlan & Stewart. p. 150. Retrieved 6 April 2016.
  33. ^ "Who's who in the Far East, 1906–7, June". Internet Archive. Hongkong: China Mail. 1906. p. 204. Retrieved 6 April 2016.
  34. ^ 'Parishes: Sherfield English', in A History of the County of Hampshire: Volume 4, ed. William Page (London, 1911), pp. 510–511. British History Online http://www.british-history.ac.uk/vch/hants/vol4/pp510-511 [accessed 6 April 2016].
  35. ^ "Marriages". Westmeath Journal. 29 May 1828. p. 3. Retrieved 6 April 2016.
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