'Some Disputes of Consequence': Maclaurin among the Molasses Barrels

Social Studies of Science

Volumn 28, Issue 1, 1998, Pages 139-168

  Grabiner, Judith V ^a  

^a PITZER COLLEGE   (United States)

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[No Author keywords available]

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EID: 0032376919     PISSN: 03063127     EISSN: None     Source Type: Journal    
DOI: 10.1177/030631298028001005     Document Type: Article

References (200)

1. Colin Maclaurin, A Treatise of Fluxions in Two Books (Edinburgh: Ruddimans, 1742), 1. This quotation is from the first sentence of the Introduction to that edition.
2. On Maclaurin's mathematical career and influence, see Erik Lars Sageng, Colin MacLaurin and the Foundations of the Method of Fluxions (Princeton, NJ: unpublished PhD dissertation, Princeton University, 1989); Judith V. Grabiner, 'Was Newton's Calculus a Dead End?: The Continental Influence of Maclaurin's Treatise of Fluxions', American Mathematical Monthly, Vol. 104 (1997), 393-410; H.W. Turnbull, Bicentenary of the Death of Colin Maclaurin (1698-1746) (Aberdeen: The University Press, 1951); Charles Tweedie, 'A Study of the Life and Writings of Colin Maclaurin', Mathematical Gazette, Vol. 8 (1915), 132-51. On Maclaurin's promotion of the applications of science, see also Roger L. Emerson, 'The Philosophical Society of Edinburgh, 1737-1747', British Journal for the History of Science, Vol. 12 (1979), 154-91. There is some ambiguity over the spelling of Maclaurin's surname: I will use the lower case '1', unless it is capitalized in sources I quote.
3. On Maclaurin's mathematical career and influence, see Erik Lars Sageng, Colin MacLaurin and the Foundations of the Method of Fluxions (Princeton, NJ: unpublished PhD dissertation, Princeton University, 1989); Judith V. Grabiner, 'Was Newton's Calculus a Dead End?: The Continental Influence of Maclaurin's Treatise of Fluxions', American Mathematical Monthly, Vol. 104 (1997), 393-410; H.W. Turnbull, Bicentenary of the Death of Colin Maclaurin (1698-1746) (Aberdeen: The University Press, 1951); Charles Tweedie, 'A Study of the Life and Writings of Colin Maclaurin', Mathematical Gazette, Vol. 8 (1915), 132-51. On Maclaurin's promotion of the applications of science, see also Roger L. Emerson, 'The Philosophical Society of Edinburgh, 1737-1747', British Journal for the History of Science, Vol. 12 (1979), 154-91. There is some ambiguity over the spelling of Maclaurin's surname: I will use the lower case '1', unless it is capitalized in sources I quote.
4. On Maclaurin's mathematical career and influence, see Erik Lars Sageng, Colin MacLaurin and the Foundations of the Method of Fluxions (Princeton, NJ: unpublished PhD dissertation, Princeton University, 1989); Judith V. Grabiner, 'Was Newton's Calculus a Dead End?: The Continental Influence of Maclaurin's Treatise of Fluxions', American Mathematical Monthly, Vol. 104 (1997), 393-410; H.W. Turnbull, Bicentenary of the Death of Colin Maclaurin (1698-1746) (Aberdeen: The University Press, 1951); Charles Tweedie, 'A Study of the Life and Writings of Colin Maclaurin', Mathematical Gazette, Vol. 8 (1915), 132-51. On Maclaurin's promotion of the applications of science, see also Roger L. Emerson, 'The Philosophical Society of Edinburgh, 1737-1747', British Journal for the History of Science, Vol. 12 (1979), 154-91. There is some ambiguity over the spelling of Maclaurin's surname: I will use the lower case '1', unless it is capitalized in sources I quote.
5. On Maclaurin's mathematical career and influence, see Erik Lars Sageng, Colin MacLaurin and the Foundations of the Method of Fluxions (Princeton, NJ: unpublished PhD dissertation, Princeton University, 1989); Judith V. Grabiner, 'Was Newton's Calculus a Dead End?: The Continental Influence of Maclaurin's Treatise of Fluxions', American Mathematical Monthly, Vol. 104 (1997), 393-410; H.W. Turnbull, Bicentenary of the Death of Colin Maclaurin (1698-1746) (Aberdeen: The University Press, 1951); Charles Tweedie, 'A Study of the Life and Writings of Colin Maclaurin', Mathematical Gazette, Vol. 8 (1915), 132-51. On Maclaurin's promotion of the applications of science, see also Roger L. Emerson, 'The Philosophical Society of Edinburgh, 1737-1747', British Journal for the History of Science, Vol. 12 (1979), 154-91. There is some ambiguity over the spelling of Maclaurin's surname: I will use the lower case '1', unless it is capitalized in sources I quote.
6. On Maclaurin's mathematical career and influence, see Erik Lars Sageng, Colin MacLaurin and the Foundations of the Method of Fluxions (Princeton, NJ: unpublished PhD dissertation, Princeton University, 1989); Judith V. Grabiner, 'Was Newton's Calculus a Dead End?: The Continental Influence of Maclaurin's Treatise of Fluxions', American Mathematical Monthly, Vol. 104 (1997), 393-410; H.W. Turnbull, Bicentenary of the Death of Colin Maclaurin (1698-1746) (Aberdeen: The University Press, 1951); Charles Tweedie, 'A Study of the Life and Writings of Colin Maclaurin', Mathematical Gazette, Vol. 8 (1915), 132-51. On Maclaurin's promotion of the applications of science, see also Roger L. Emerson, 'The Philosophical Society of Edinburgh, 1737-1747', British Journal for the History of Science, Vol. 12 (1979), 154-91. There is some ambiguity over the spelling of Maclaurin's surname: I will use the lower case '1', unless it is capitalized in sources I quote.
7. There is an extensive literature on the use of mathematics to establish formal procedures to regulate social interaction. See first the synthesis in Theodore Porter, Trust in Numbers: The Pursuit of Objectivity in Science and Public Life (Princeton, NJ: Princeton University Press, 1995). See also M. Norton Wise (ed.), The Values of Precision (Princeton, NJ: Princeton University Press, 1995); Tore Frängsmyr, John L. Heilbron and Robin E. Rider (eds), The Quantifying Spirit in the Eighteenth Century (Berkeley & Los Angeles, CA: University of California Press, 1990); and the Symposium on 'The Social History of Objectivity', Social Studies of Science, Vol. 22, No. 4 (November 1992), 595-651, especially Lorraine Daston, 'Objectivity and the Escape from Perspective', 597-618, and Theodore Porter, 'Quantification and the Accounting Ideal in Science', 633-51. Two case studies on topics related to that of the present paper, though at later dates, are Simon Schaffer, 'Accurate Measurement is an English Science', in Wise (ed.), op. cit., 135-72, and Otto Sibum, 'Reworking the Mechanical Value of Heat: Instruments of Precision and Gestures of Accuracy in Early Victorian England', Studies in History and Philosophy of Science, Vol. 26 (1995), 73-106.
8. There is an extensive literature on the use of mathematics to establish formal procedures to regulate social interaction. See first the synthesis in Theodore Porter, Trust in Numbers: The Pursuit of Objectivity in Science and Public Life (Princeton, NJ: Princeton University Press, 1995). See also M. Norton Wise (ed.), The Values of Precision (Princeton, NJ: Princeton University Press, 1995); Tore Frängsmyr, John L. Heilbron and Robin E. Rider (eds), The Quantifying Spirit in the Eighteenth Century (Berkeley & Los Angeles, CA: University of California Press, 1990); and the Symposium on 'The Social History of Objectivity', Social Studies of Science, Vol. 22, No. 4 (November 1992), 595-651, especially Lorraine Daston, 'Objectivity and the Escape from Perspective', 597-618, and Theodore Porter, 'Quantification and the Accounting Ideal in Science', 633-51. Two case studies on topics related to that of the present paper, though at later dates, are Simon Schaffer, 'Accurate Measurement is an English Science', in Wise (ed.), op. cit., 135-72, and Otto Sibum, 'Reworking the Mechanical Value of Heat: Instruments of Precision and Gestures of Accuracy in Early Victorian England', Studies in History and Philosophy of Science, Vol. 26 (1995), 73-106.
9. There is an extensive literature on the use of mathematics to establish formal procedures to regulate social interaction. See first the synthesis in Theodore Porter, Trust in Numbers: The Pursuit of Objectivity in Science and Public Life (Princeton, NJ: Princeton University Press, 1995). See also M. Norton Wise (ed.), The Values of Precision (Princeton, NJ: Princeton University Press, 1995); Tore Frängsmyr, John L. Heilbron and Robin E. Rider (eds), The Quantifying Spirit in the Eighteenth Century (Berkeley & Los Angeles, CA: University of California Press, 1990); and the Symposium on 'The Social History of Objectivity', Social Studies of Science, Vol. 22, No. 4 (November 1992), 595-651, especially Lorraine Daston, 'Objectivity and the Escape from Perspective', 597-618, and Theodore Porter, 'Quantification and the Accounting Ideal in Science', 633-51. Two case studies on topics related to that of the present paper, though at later dates, are Simon Schaffer, 'Accurate Measurement is an English Science', in Wise (ed.), op. cit., 135-72, and Otto Sibum, 'Reworking the Mechanical Value of Heat: Instruments of Precision and Gestures of Accuracy in Early Victorian England', Studies in History and Philosophy of Science, Vol. 26 (1995), 73-106.
10. There is an extensive literature on the use of mathematics to establish formal procedures to regulate social interaction. See first the synthesis in Theodore Porter, Trust in Numbers: The Pursuit of Objectivity in Science and Public Life (Princeton, NJ: Princeton University Press, 1995). See also M. Norton Wise (ed.), The Values of Precision (Princeton, NJ: Princeton University Press, 1995); Tore Frängsmyr, John L. Heilbron and Robin E. Rider (eds), The Quantifying Spirit in the Eighteenth Century (Berkeley & Los Angeles, CA: University of California Press, 1990); and the Symposium on 'The Social History of Objectivity', Social Studies of Science, Vol. 22, No. 4 (November 1992), 595-651, especially Lorraine Daston, 'Objectivity and the Escape from Perspective', 597-618, and Theodore Porter, 'Quantification and the Accounting Ideal in Science', 633-51. Two case studies on topics related to that of the present paper, though at later dates, are Simon Schaffer, 'Accurate Measurement is an English Science', in Wise (ed.), op. cit., 135-72, and Otto Sibum, 'Reworking the Mechanical Value of Heat: Instruments of Precision and Gestures of Accuracy in Early Victorian England', Studies in History and Philosophy of Science, Vol. 26 (1995), 73-106.
11. There is an extensive literature on the use of mathematics to establish formal procedures to regulate social interaction. See first the synthesis in Theodore Porter, Trust in Numbers: The Pursuit of Objectivity in Science and Public Life (Princeton, NJ: Princeton University Press, 1995). See also M. Norton Wise (ed.), The Values of Precision (Princeton, NJ: Princeton University Press, 1995); Tore Frängsmyr, John L. Heilbron and Robin E. Rider (eds), The Quantifying Spirit in the Eighteenth Century (Berkeley & Los Angeles, CA: University of California Press, 1990); and the Symposium on 'The Social History of Objectivity', Social Studies of Science, Vol. 22, No. 4 (November 1992), 595-651, especially Lorraine Daston, 'Objectivity and the Escape from Perspective', 597-618, and Theodore Porter, 'Quantification and the Accounting Ideal in Science', 633-51. Two case studies on topics related to that of the present paper, though at later dates, are Simon Schaffer, 'Accurate Measurement is an English Science', in Wise (ed.), op. cit., 135-72, and Otto Sibum, 'Reworking the Mechanical Value of Heat: Instruments of Precision and Gestures of Accuracy in Early Victorian England', Studies in History and Philosophy of Science, Vol. 26 (1995), 73-106.
12. There is an extensive literature on the use of mathematics to establish formal procedures to regulate social interaction. See first the synthesis in Theodore Porter, Trust in Numbers: The Pursuit of Objectivity in Science and Public Life (Princeton, NJ: Princeton University Press, 1995). See also M. Norton Wise (ed.), The Values of Precision (Princeton, NJ: Princeton University Press, 1995); Tore Frängsmyr, John L. Heilbron and Robin E. Rider (eds), The Quantifying Spirit in the Eighteenth Century (Berkeley & Los Angeles, CA: University of California Press, 1990); and the Symposium on 'The Social History of Objectivity', Social Studies of Science, Vol. 22, No. 4 (November 1992), 595-651, especially Lorraine Daston, 'Objectivity and the Escape from Perspective', 597-618, and Theodore Porter, 'Quantification and the Accounting Ideal in Science', 633-51. Two case studies on topics related to that of the present paper, though at later dates, are Simon Schaffer, 'Accurate Measurement is an English Science', in Wise (ed.), op. cit., 135-72, and Otto Sibum, 'Reworking the Mechanical Value of Heat: Instruments of Precision and Gestures of Accuracy in Early Victorian England', Studies in History and Philosophy of Science, Vol. 26 (1995), 73-106.
13. There is an extensive literature on the use of mathematics to establish formal procedures to regulate social interaction. See first the synthesis in Theodore Porter, Trust in Numbers: The Pursuit of Objectivity in Science and Public Life (Princeton, NJ: Princeton University Press, 1995). See also M. Norton Wise (ed.), The Values of Precision (Princeton, NJ: Princeton University Press, 1995); Tore Frängsmyr, John L. Heilbron and Robin E. Rider (eds), The Quantifying Spirit in the Eighteenth Century (Berkeley & Los Angeles, CA: University of California Press, 1990); and the Symposium on 'The Social History of Objectivity', Social Studies of Science, Vol. 22, No. 4 (November 1992), 595-651, especially Lorraine Daston, 'Objectivity and the Escape from Perspective', 597-618, and Theodore Porter, 'Quantification and the Accounting Ideal in Science', 633-51. Two case studies on topics related to that of the present paper, though at later dates, are Simon Schaffer, 'Accurate Measurement is an English Science', in Wise (ed.), op. cit., 135-72, and Otto Sibum, 'Reworking the Mechanical Value of Heat: Instruments of Precision and Gestures of Accuracy in Early Victorian England', Studies in History and Philosophy of Science, Vol. 26 (1995), 73-106.
14. There is an extensive literature on the use of mathematics to establish formal procedures to regulate social interaction. See first the synthesis in Theodore Porter, Trust in Numbers: The Pursuit of Objectivity in Science and Public Life (Princeton, NJ: Princeton University Press, 1995). See also M. Norton Wise (ed.), The Values of Precision (Princeton, NJ: Princeton University Press, 1995); Tore Frängsmyr, John L. Heilbron and Robin E. Rider (eds), The Quantifying Spirit in the Eighteenth Century (Berkeley & Los Angeles, CA: University of California Press, 1990); and the Symposium on 'The Social History of Objectivity', Social Studies of Science, Vol. 22, No. 4 (November 1992), 595-651, especially Lorraine Daston, 'Objectivity and the Escape from Perspective', 597-618, and Theodore Porter, 'Quantification and the Accounting Ideal in Science', 633-51. Two case studies on topics related to that of the present paper, though at later dates, are Simon Schaffer, 'Accurate Measurement is an English Science', in Wise (ed.), op. cit., 135-72, and Otto Sibum, 'Reworking the Mechanical Value of Heat: Instruments of Precision and Gestures of Accuracy in Early Victorian England', Studies in History and Philosophy of Science, Vol. 26 (1995), 73-106.
15. Daston, op. cit. note 3, 607.
16. Theodore Porter, 'Precision and Trust: Early Victorian Insurance and the Politics of Calculation', in Wise (ed.), op. cit. note 3, 173-97, at 192.
17. Patrick Murdoch, 'An Account of the Life and Writings of the Author', in Colin Maclaurin, Account of Sir Isaac Newton's Philosophical Discoveries (London, 1748; reprinted New York: Johnson Reprint Corp., 1968), i-xx, at xix. The 'two elaborate memorials' are the two copies of the manuscript described in note 8 below.
18. John J. McCusker and Russell R. Menard, The Economy of British America, 1607-1789 (Chapel Hill, NC & London: University of North Carolina Press, 1985), 289.
19. C. Maclaurin, Memorial offered to the Honourable Commissioners of Excise concerning the Mensuration of Tuns or Backs that have some irregularity in the Figure and Situation of the Bottom, and in the Height and Position of the Staves; and of ascertaining a just place for taking the dry Inches in such a Vessel: To which is added a Method of correcting the common Tables, and some new Theorems concerning the Mensuration of regular Solids (Manuscript, National Library of Scotland Adv MS 23.1.13), 2. All page citations will be to this copy, whose page numbers are reproduced in my published version: J.V. Grabiner, 'A Mathematician Among the Molasses Barrels: Maclaurin's Unpublished Memoir on Volumes', Proceedings of the Edinburgh Mathematical Society, Vol. 39 (1996), 193-240. There is another manuscript copy in a different hand (neither hand is Maclaurin's), with slightly different spelling and pagination but the same content, in the Edinburgh University Library, DC. 1.17.
20. C. Maclaurin, Memorial offered to the Honourable Commissioners of Excise concerning the Mensuration of Tuns or Backs that have some irregularity in the Figure and Situation of the Bottom, and in the Height and Position of the Staves; and of ascertaining a just place for taking the dry Inches in such a Vessel: To which is added a Method of correcting the common Tables, and some new Theorems concerning the Mensuration of regular Solids (Manuscript, National Library of Scotland Adv MS 23.1.13), 2. All page citations will be to this copy, whose page numbers are reproduced in my published version: J.V. Grabiner, 'A Mathematician Among the Molasses Barrels: Maclaurin's Unpublished Memoir on Volumes', Proceedings of the Edinburgh Mathematical Society, Vol. 39 (1996), 193-240. There is another manuscript copy in a different hand (neither hand is Maclaurin's), with slightly different spelling and pagination but the same content, in the Edinburgh University Library, DC. 1.17.
21. It involves at least nine steps: preparing the staves, raising the cask, trussing and bending, topping or making the chime, cleaning down, bunging, heading, caulking or flagging, and finally fitting the hoops: see J. Geraint Jenkins and R.A. Salamon, 'A Note on Coopering', in Charles Singer et al. (eds), A History of Technology (Oxford: Clarendon Press, 1957), Vol. III, 128-33.
22. Denis Diderot and Jean d'Alembert, Encyclopédie ou dictionnaire raisonné des sciences, des arts et des métiers (28 Vols., Paris, 1751-72), Vol. X, s.v. 'Tonnelier', Plate I.
23. Maclaurin, op. cit. note 8, 9-10, 16, 36, 43, 54-57, 65, 82. Some error-estimates in gallons are explicitly given by Maclaurin; others can readily be calculated from information he gave.
24. Ibid., 1. The quotation clearly illustrates a remark of Theodore Porter, that the 'insistence on standardizability, even where it violates the best judgment of expert practitioners, will rarely be found except in fields that are highly vulnerable to criticism from outsiders': Porter (1992), op. cit. note 3, 639.
25. Henry Atton and Henry Hurst Holland, The King's Customs: An Account of Maritime Revenue and Contraband Traffic in England, Scotland, and Ireland, from the Earliest Times to theYear 1800 [1908] (London: Frank Cass, 1967), 110; Graham Smith, 'A Poor, Damn'd, Rascally Gager': Robert Burns the Exciseman (Ayr: Alloway Publishing, 1989), 51-52.
26. Henry Atton and Henry Hurst Holland, The King's Customs: An Account of Maritime Revenue and Contraband Traffic in England, Scotland, and Ireland, from the Earliest Times to theYear 1800 [1908] (London: Frank Cass, 1967), 110; Graham Smith, 'A Poor, Damn'd, Rascally Gager': Robert Burns the Exciseman (Ayr: Alloway Publishing, 1989), 51-52.
27. A recalculation which would have been 'evidently [in] the Traders interest': Maclaurin, op. cit. note 8, 82.
28. Ibid., 15.
29. Charles Leadbetter, The Royal Gauger, or Gauging Made Perfectly Easy, as it is Actually Practised by the Officers of His Majesty's Revenue of Excise [1739] (London: E. Wicksted, rev. edn, 1755), 129.
30. Maclaurin, op. cit. note 8, 7-8.
31. This was because, he said, it was harder to find the greatest dip than to find the places where the opposite dipstick readings are equal, since 'the dip does not vary sensibly from a considerable space there. . . . But the dip varys most sensibly in a little space at the quarters': ibid., 40. Such reasoning is common in the analysis of maxima and minima in the calculus.
32. Ibid., 65.
33. Ibid., 80.
34. Ibid., 59-61. The maximum error is given as 1.196 gallons in Maclaurin's table, ibid., 63; I have calculated the average from his data. The process Maclaurin was criticizing was called 'inching the Tun', and was standard throughout the excise: see Leadbetter, op. cit. note 16, 126-27.
35. Maclaurin observed elsewhere that this method was common among traders and tax collectors: 'In general it is usual to measure any round vessel, by distinguishing it into several frustums, and taking the diameter of the section at the middle of each frustum, thence to compute the content of each, as if it was a cylinder of that mean diameter; and to give their sum as the content of the vessel . . . and in this manner [to] calculate a table for the vessel'; the table will tell the amount of liquid in the vessel when a dipstick finds the 'wet inches' (height of the liquid) or the 'dry inches' (height of the section of the vessel above the liquid) - always, Maclaurin added, 'having regard to the inclination . . . of the vessel when it has any': David Gregory, A Treatise of Practical Geometry, Translated [anon.] from the Latin, with Additions [by Colin Maclaurin] (Edinburgh: Ruddimans, 1745), 146. Cf. Leadbetter, op. cit. note 16, 126, 141, 145.
36. Maclaurin, op. cit. note 8, 67. This result, among other things, lets him find the error in the tables computed by the 'usual method', as discussed above.
37. For the sphere, see ibid., 76. For the spheroid, the difference between the cylinder and the frustum is like that for the sphere multiplied by the ratio of the square of the horizontal axis and the vertical axis of the generating ellipse: ibid., 77. For the hyperboloid, the cylinder is smaller than the frustum but the magnitude of the difference is the same as for the spheroid, and also equals the difference one obtains for the frustum of the cone with the same height generated by rotating the asymptotes of the hyperbola: ibid., 79-80.
38. Ibid., 80.
39. Maclaurin, op. cit. note 1, 24-26.
40. Maclaurin, op. cit. note 8, 81.
41. Maclaurin had sent Simson the introduction (the first part he finished) to his Treatise of Fluxions. Simson's comment is in a letter of 27 July 1736: see Stella Mills (ed.), The Collected Letters of Colin MacLaurin (Nantwich, Ches.: Shiva Publishing, 1982), 255.
42. Maclaurin, op. cit. note 8, 81.
43. Ibid., 91-94. A slightly improved version of the calculus proofs appears in Maclaurin, op. cit. note 1, 62.
44. To closer than 1/40th of a gallon: Maclaurin, op. cit. note 8, 62.
45. Murdoch, op. cit. note 6, xix. Unfortunately one cannot view the Excise Commission's reception of Maclaurin's Memorial, because the Minute Books of the Scottish Excise Board for this period have not survived: Richard Scott, The Politics and Administration of Scotland, 1725-1748 (unpublished PhD Thesis, University of Edinburgh, 1981), 570; Scottish Record Office, conversations with several archivists. The quotation given from Murdoch (save for the word 'likewise') appears also (without acknowledgment) in the anonymous biography of Maclaurin in the second edition of the Treatise of Fluxions: Colin Maclaurin, A Treatise of Fluxions in Two Volumes, by Colin Maclaurin. Second Edition, to which is prefixed an Account of His Life. The Whole Carefully Corrected and Revised by an Eminent Mathematician (London: William Baynes & William Davis, 1801). This anonymous biography was taken virtually verbatim from Charles Hutton, A Mathematical and Philosophical Dictionary in Two Volumes (London: J. Johnson, G.G. & J. Robinson, 1795-96), s.v. 'Maclaurin, Colin', Vol. 2, 60-61. Presumably Hutton was the 'eminent mathematician' of the 1801 title page. In any case, Hutton's biography of Maclaurin, though shorter than Murdoch's, would be viewed today as having been plagiarized from it.
46. Murdoch, op. cit. note 6, xix. Unfortunately one cannot view the Excise Commission's reception of Maclaurin's Memorial, because the Minute Books of the Scottish Excise Board for this period have not survived: Richard Scott, The Politics and Administration of Scotland, 1725-1748 (unpublished PhD Thesis, University of Edinburgh, 1981), 570; Scottish Record Office, conversations with several archivists. The quotation given from Murdoch (save for the word 'likewise') appears also (without acknowledgment) in the anonymous biography of Maclaurin in the second edition of the Treatise of Fluxions: Colin Maclaurin, A Treatise of Fluxions in Two Volumes, by Colin Maclaurin. Second Edition, to which is prefixed an Account of His Life. The Whole Carefully Corrected and Revised by an Eminent Mathematician (London: William Baynes & William Davis, 1801). This anonymous biography was taken virtually verbatim from Charles Hutton, A Mathematical and Philosophical Dictionary in Two Volumes (London: J. Johnson, G.G. & J. Robinson, 1795-96), s.v. 'Maclaurin, Colin', Vol. 2, 60-61. Presumably Hutton was the 'eminent mathematician' of the 1801 title page. In any case, Hutton's biography of Maclaurin, though shorter than Murdoch's, would be viewed today as having been plagiarized from it.
47. Murdoch, op. cit. note 6, xix. Unfortunately one cannot view the Excise Commission's reception of Maclaurin's Memorial, because the Minute Books of the Scottish Excise Board for this period have not survived: Richard Scott, The Politics and Administration of Scotland, 1725-1748 (unpublished PhD Thesis, University of Edinburgh, 1981), 570; Scottish Record Office, conversations with several archivists. The quotation given from Murdoch (save for the word 'likewise') appears also (without acknowledgment) in the anonymous biography of Maclaurin in the second edition of the Treatise of Fluxions: Colin Maclaurin, A Treatise of Fluxions in Two Volumes, by Colin Maclaurin. Second Edition, to which is prefixed an Account of His Life. The Whole Carefully Corrected and Revised by an Eminent Mathematician (London: William Baynes & William Davis, 1801). This anonymous biography was taken virtually verbatim from Charles Hutton, A Mathematical and Philosophical Dictionary in Two Volumes (London: J. Johnson, G.G. & J. Robinson, 1795-96), s.v. 'Maclaurin, Colin', Vol. 2, 60-61. Presumably Hutton was the 'eminent mathematician' of the 1801 title page. In any case, Hutton's biography of Maclaurin, though shorter than Murdoch's, would be viewed today as having been plagiarized from it.
48. Murdoch, op. cit. note 6, xix. Unfortunately one cannot view the Excise Commission's reception of Maclaurin's Memorial, because the Minute Books of the Scottish Excise Board for this period have not survived: Richard Scott, The Politics and Administration of Scotland, 1725-1748 (unpublished PhD Thesis, University of Edinburgh, 1981), 570; Scottish Record Office, conversations with several archivists. The quotation given from Murdoch (save for the word 'likewise') appears also (without acknowledgment) in the anonymous biography of Maclaurin in the second edition of the Treatise of Fluxions: Colin Maclaurin, A Treatise of Fluxions in Two Volumes, by Colin Maclaurin. Second Edition, to which is prefixed an Account of His Life. The Whole Carefully Corrected and Revised by an Eminent Mathematician (London: William Baynes & William Davis, 1801). This anonymous biography was taken virtually verbatim from Charles Hutton, A Mathematical and Philosophical Dictionary in Two Volumes (London: J. Johnson, G.G. & J. Robinson, 1795-96), s.v. 'Maclaurin, Colin', Vol. 2, 60-61. Presumably Hutton was the 'eminent mathematician' of the 1801 title page. In any case, Hutton's biography of Maclaurin, though shorter than Murdoch's, would be viewed today as having been plagiarized from it.
49. Letter of 18 November 1735: Mills, op. cit. note 28, 67-68.
50. Richard B. Sheridan, Sugar and Slavery: An Economic History of the British West Indies, 1623-1775 (Barbados: Caribbean Universities Press, 1974), 339.
51. Ibid., 29; Sidney W. Mintz, Sweetness and Power: The Place of Sugar in Modern History (New York: Viking, 1985), 114.
52. Carole Shammas, The Pre-Industrial Consumer in England and America (Oxford: Clarendon Press, 1990), 81-82.
53. Duncan Forbes, Some Considerations on the Present State of Scotland (Edinburgh: W. Sands, 1744), 7. (Forbes did not approve of the consumption of foreign goods like cane sugar.) I owe this reference to Mintz, op. cit. note 35, 114. Punch is generally made with rum.
54. Sheridan, op. cit. note 34, 344.
55. Atton & Holland, op. cit. note 13, 102.
56. Norman Longmate, The Waterdrinkers: A History of Temperance (London: Hamish Hamilton, 1968), 9-10.
57. Sheridan, op. cit. note 34, 345.
58. Mintz, op. cit. note 35, 170.
59. Atton & Holland, op. cit. note 13, 206.
60. Sheridan, op. cit. note 34, 74.
61. Harold A. Innis, The Cod Fisheries: The History of an International Economy (Toronto: University of Toronto Press, 1954), 165.
62. Sheridan, op. cit. note 34, 347.
63. McCusker & Menard, op. cit. note 7, 156.
64. Ibid., 155, 315.
65. Robin Blackburn, The Making of New World Slavery: From the Baroque to the Modern, 1492-1800 (London & New York: Verso, 1997), 260.
66. Mintz, op. cit. note 35, 52.
67. Sheridan, op. cit. note 34, 242.
68. Blackburn, op. cit. note 49, 380.
69. Ibid., 411.
70. Ibid., 260.
71. Reproduced by permission of the British Library. Mintz, op. cit. note 35, reprints this picture following his p.78, and observes there that, though dated 1823, the 'highly organized, almost industrial character of field labor' it portrays could have been witnessed even earlier.
72. John Gibson, quoted by Henry Hamilton, An Economic History of Scotland in the Eighteenth Century (Oxford: Clarendon Press, 1963), 261; cf. David Daiches, Glasgow (London: Andre Deutsch, 1977), 53.
73. John Gibson, quoted by Henry Hamilton, An Economic History of Scotland in the Eighteenth Century (Oxford: Clarendon Press, 1963), 261; cf. David Daiches, Glasgow (London: Andre Deutsch, 1977), 53.
74. Treaty of Union, quoted in Bruce Lenman, An Economic History of Modern Scotland, 1660-1976 (London: B.T. Batsford, 1977), 58.
75. James D. Marwick, The River Clyde and the Clyde Burghs (Glasgow: James Maclehose & Sons, 1909), 160.
76. Lenman, op. cit. note 57, 91.
77. Sheridan, op. cit. note 34, 31.
78. Quoted in Daiches, op. cit. note 56, 47.
79. Charles A. Oakley, The Second City (London & Glasgow: Blackie & Son, 1946), 9.
80. Sheridan, op. cit. note 34, 31. The last sugar refinery in Scotland closed in July 1995.
81. Hamilton, op. cit. note 56, 256.
82. Ibid., 259.
83. Oakley, op. cit. note 62, 9.
84. Leslie A. Clarkson, The Pre-Industrial Economy in England, 1500-1750 (London, B.T. Batsford, 1971), 93.
85. Ibid., 188. Cf. John Brewer, The Sinews of Power: War, Money and the English State, 1688-1783 (London: Unwin Hyman, 1989), 95-99.
86. Elizabeth Evelynola Hoon, The Organization of the English Customs System, 1696-1766 (Newton Abbott, Devon: David & Charles, 1968), xix.
87. Charles Davenant, 'Essay on Ways and Means of Supplying the War' (London, 1695), in C. Davenant, The Political and Commercial Works, ed. Sir Charles Whitworth (London, 1771), Vol. I, 1-81, at 62. On Davenant's application of quantitative methods to economic and social questions, see Mark Blaug (ed.), Pre-Classical Economists, Vol. I, No. 6: Charles Davenant (1656-1714) and William Petty (1623-1687) (Great Yarmouth, Norfolk: Galliard, 1991).
88. Charles Davenant, 'Essay on Ways and Means of Supplying the War' (London, 1695), in C. Davenant, The Political and Commercial Works, ed. Sir Charles Whitworth (London, 1771), Vol. I, 1-81, at 62. On Davenant's application of quantitative methods to economic and social questions, see Mark Blaug (ed.), Pre-Classical Economists, Vol. I, No. 6: Charles Davenant (1656-1714) and William Petty (1623-1687) (Great Yarmouth, Norfolk: Galliard, 1991).
89. Brewer, op. cit. note 68, 101.
90. Ibid., xv-xvi.
91. Ibid., 94, 225.
92. Ibid., 105.
93. Ibid., 108-10.
94. Ibid., 109-10.
95. Ibid., 113.
96. Ibid., 113-14.
97. Ibid., 221-22.
98. Ibid., 223.
99. Charles Davenant, 'Discourses on the Public Revenues, and on Trade', Part I (London, 1698), in Davenant, op. cit. note 70, Vol. I, 125-342, at 215.
100. Brewer, op. cit. note 68, 114.
101. Clarkson, op. cit. note 67, 204.
102. Lenman, op. cit. note 57, 61.
103. The Scots were to be given monetary compensation equal to the increase in customs and excise revenue until 1714: Lenman, op. cit. note 57, 59.
104. Ibid., 59-61.
105. Hamilton, op. cit. note 56, 265. In fact the 18th century was when the smuggling of large quantities first became profitable; before, duties had been lower, fewer goods were being traded, and it had been harder to run contraband in the square-rigged ships of the day, which were less manœuvrable than those rigged fore and aft: see Edward Carson, The Ancient and Rightful Customs: A History of the English Customs Service (London: Faber & Faber, 1972), 55-56.
106. T. Christopher Smout, A History of the Scottish People, 1560-1830 (London: Fontana, 1985; reprint of edition published London: Collins, 1969), 210.
107. Rosalind Mitchison, A History of Scotland (London: Routledge, 2nd edn, 1982), 326.
108. Lenman, op. cit. note 57, 64.
109. Vaughan, a Welshman appointed to the Customs Commission in Scotland in 1728, was already associated with Walpole - and with the Earl of Islay, whose importance will be discussed later.
110. Jacob M. Price, 'The Excise Affair Revisited: The Administrative and Colonial Dimensions of a Parliamentary Crisis', in Stephen B. Baxter (ed.), England's Rise to Greatness, 1660-1763 (Berkeley & Los Angeles, CA: University of California Press, 1983), 257-321, at 289-92.
111. Maclaurin, letter to Lord Hamilton of Dalzell, in Mills (ed.), op. cit. note 28, 55.
112. The story is dramatically recounted in Walter Scott's novel The Heart of Midlothian. Smout (op. cit. note 88, 498n) calls Scott's 'the best account', adding: 'There has probably never been so brilliant a piece of historical research so brilliantly disguised as fiction'.
113. Keith M. Baker, 'Science and Politics at the End of the Old Regime', in Baker, Inventing the French Revolution: Essays in French Political Culture in the Eighteenth Century (Cambridge: Cambridge University Press, 1990), 156-66, at 157.
114. Atton & Holland, op. cit. note 13, 24n.
115. Ibid., 110.
116. Henry Phillippes, A Mathematical Manual (London: M. Clark, 1683); Atton & Holland, op. cit. note 13, 110.
117. Ibid. In March 1707, the wine gallon was legally declared to be 231 cubic inches (Act 5 Anne c 17, § 17 of 1706), or a cylinder 7" in diameter and 6" deep (which effectively legislates π = 22/7); Robert Dickson O'Connor, The Weights and Measures of England (London: HMSO, 1987), 163. This legislation remained in force until 1824. As part of his drive toward standardization, Maclaurin explained the relationship between this gallon and 'the Scots pint, according to the ordinary Pewterer's Juggs': op. cit. note 8, Prop. XXVIII, 83.
118. Atton & Holland, op. cit. note 13, 110.
119. In Defoe's History of the Union of Great Britain (Edinburgh: Anderson, 1709); quoted in Francis Wilkins, Scottish Customs and Excise Records, with Particular Reference to Strathclyde (Kidderminster, Worcs.:Wyre Forest Press, 1992), 8.
120. In Defoe's History of the Union of Great Britain (Edinburgh: Anderson, 1709); quoted in Francis Wilkins, Scottish Customs and Excise Records, with Particular Reference to Strathclyde (Kidderminster, Worcs.:Wyre Forest Press, 1992), 8.
121. J.L. Heilbron, 'The Measure of Enlightenment', in Frängsmyr, Heilbron & Rider (eds), op. cit. note 3, 197-242, at 209-10.
122. Witold Kula, Measures and Men, trans. Richard Szreter (Princeton, NJ: Princeton University Press, 1986), 118.
123. Ibid., 219, 205.
124. Sibum, op. cit. note 3, 86.
125. Kula, op. cit. note 103, 118.
126. John Pink, The Excise Officers and their Duties in an English Market Town: Kingston upon Thames, 1643-1973 (Surbiton, Surrey: JRP, 1996), 16.
127. I thank Tom Koerner for reminding me of this.
128. Charles Dickens, Hard Times: For These Times (London: Bradbury & Evans, 1854), Book III, Chapter I, 263: thank Reviel Netz for this reference. For a discussion of the types of excise rods, both for measurement and for slide-rule calculation, see John Owens, Plain Papers Relating to the Excise Branch of the Inland Revenue Department from 1621 to 1878 (Linlithgow, 1879), s.v. 'Gauging Appliances', 252-59. These instruments, like other standardized devices, enable the replication of results; the slide rules, for instance, had special constants and scales which embodied various rules for calculating volumes. See the extensive discussions of such slide rules in Charles Hutton, A Treatise on Mensuration both in Theory and Practice (Newcastle-upon-Tyne: T. Saint, 1770), 511-26, and in Robert Shirtcliffe, The Theory and Practice of Gauging (London: H. Woodfall, 1740), 33-55.
129. Charles Dickens, Hard Times: For These Times (London: Bradbury & Evans, 1854), Book III, Chapter I, 263: thank Reviel Netz for this reference. For a discussion of the types of excise rods, both for measurement and for slide-rule calculation, see John Owens, Plain Papers Relating to the Excise Branch of the Inland Revenue Department from 1621 to 1878 (Linlithgow, 1879), s.v. 'Gauging Appliances', 252-59. These instruments, like other standardized devices, enable the replication of results; the slide rules, for instance, had special constants and scales which embodied various rules for calculating volumes. See the extensive discussions of such slide rules in Charles Hutton, A Treatise on Mensuration both in Theory and Practice (Newcastle-upon-Tyne: T. Saint, 1770), 511-26, and in Robert Shirtcliffe, The Theory and Practice of Gauging (London: H. Woodfall, 1740), 33-55.
130. Charles Dickens, Hard Times: For These Times (London: Bradbury & Evans, 1854), Book III, Chapter I, 263: thank Reviel Netz for this reference. For a discussion of the types of excise rods, both for measurement and for slide-rule calculation, see John Owens, Plain Papers Relating to the Excise Branch of the Inland Revenue Department from 1621 to 1878 (Linlithgow, 1879), s.v. 'Gauging Appliances', 252-59. These instruments, like other standardized devices, enable the replication of results; the slide rules, for instance, had special constants and scales which embodied various rules for calculating volumes. See the extensive discussions of such slide rules in Charles Hutton, A Treatise on Mensuration both in Theory and Practice (Newcastle-upon-Tyne: T. Saint, 1770), 511-26, and in Robert Shirtcliffe, The Theory and Practice of Gauging (London: H. Woodfall, 1740), 33-55.
131. Charles Dickens, Hard Times: For These Times (London: Bradbury & Evans, 1854), Book III, Chapter I, 263: thank Reviel Netz for this reference. For a discussion of the types of excise rods, both for measurement and for slide-rule calculation, see John Owens, Plain Papers Relating to the Excise Branch of the Inland Revenue Department from 1621 to 1878 (Linlithgow, 1879), s.v. 'Gauging Appliances', 252-59. These instruments, like other standardized devices, enable the replication of results; the slide rules, for instance, had special constants and scales which embodied various rules for calculating volumes. See the extensive discussions of such slide rules in Charles Hutton, A Treatise on Mensuration both in Theory and Practice (Newcastle-upon-Tyne: T. Saint, 1770), 511-26, and in Robert Shirtcliffe, The Theory and Practice of Gauging (London: H. Woodfall, 1740), 33-55.
132. Charles Dickens, Hard Times: For These Times (London: Bradbury & Evans, 1854), Book III, Chapter I, 263: thank Reviel Netz for this reference. For a discussion of the types of excise rods, both for measurement and for slide-rule calculation, see John Owens, Plain Papers Relating to the Excise Branch of the Inland Revenue Department from 1621 to 1878 (Linlithgow, 1879), s.v. 'Gauging Appliances', 252-59. These instruments, like other standardized devices, enable the replication of results; the slide rules, for instance, had special constants and scales which embodied various rules for calculating volumes. See the extensive discussions of such slide rules in Charles Hutton, A Treatise on Mensuration both in Theory and Practice (Newcastle-upon-Tyne: T. Saint, 1770), 511-26, and in Robert Shirtcliffe, The Theory and Practice of Gauging (London: H. Woodfall, 1740), 33-55.
133. Michael Baxendall, Painting and Experience in Fifteenth-Century Italy (Oxford: Oxford University Press, 2nd edn, 1988), 86. I thank Simon Schaffer for this reference.
134. I have found no evidence about whether either Gregory or Maclaurin knew Kepler's book, though there is a copy in the library of the University of Edinburgh; of course both men were familiar with Kepler's astronomical work. For what it is worth, Charles Hutton's Dictionary, when listing writers on gauging, includes Kepler, together with a large number of British writers: Hutton, op. cit. note 32, s.v. 'Gauging'.
135. Ad Meskens, 'Wine Gauging in Late 16th and Early 17th-Century Antwerp', Historia Mathematica, Vol. 21 (1994), 121-47.
136. Henry Crouch, A Complete View of the British Customs (London: J. Osborne & W. Bell, 1724).
137. Leadbetter, op. cit. note 16. Measures of the importance of Leadbetter's work are the many times it was reprinted, and also the large number of citations to it - for example, by Owens, op. cit. note 109, 253, 254, 255, 256, 257, 259.
138. Ibid., 126, 141, 145.
139. For instance, see Esprit Pézénas, La théorie de la pratique du jaugeage des tonneaux des navires et de leurs segments (Avignon: Jean Aubert, 2nd edn, 1788).
140. Hutton, op. cit. note 109.
141. Shirtcliffe, op. cit. note 109, 287.
142. Ibid., 197ff.
143. Derek T. Whiteside, 'Gregory', Dictionary of Scientific Biography (New York: Scribner's, 1970-77), Vol. 5, 520-23, at 521.
144. Gregory, op. cit. note 22, 3.
145. R.V. Wallis and P.J. Wallis, Bibliography of British Mathematics and Its Applications (Newcastle-upon-Tyne: Epsilon Press, 1993), Part III, and E.G.R. Taylor, Mathematical Practitioners of Hanoverian England, 1714-1840 (Cambridge: Cambridge University Press, 1966).
146. R.V. Wallis and P.J. Wallis, Bibliography of British Mathematics and Its Applications (Newcastle-upon-Tyne: Epsilon Press, 1993), Part III, and E.G.R. Taylor, Mathematical Practitioners of Hanoverian England, 1714-1840 (Cambridge: Cambridge University Press, 1966).
147. Maclaurin, op. cit. note 1, section 664, 550.
148. Taylor, op. cit. note 122, 130.
149. Ibid.
150. Maclaurin, op. cit. note 1, section 664, 550.
151. Michael Barfoot, 'Hume and the Culture of Science in the Early Eighteenth Century', in Michael A. Stewart (ed.), Studies in the Philosophy of the Scottish Enlightenment (Oxford: Clarendon Press, 1991), 151-90, at 164.
152. Ibid., 165n.
153. This is clear because the Excise Commission records document everything they paid out, from their own salaries (£500 a year) to the pittance paid to the cleaning woman: Scottish Record Office, 'Incident Charges' 1734-1736 RH 2/4/385-6, 444-46.
154. Sageng, op. cit. note 2, Chapter II, 87-162.
155. The manuscript is Colin Maclaurin, Dissertatio De Ortu Geometriae, Habita in Auditorio publico Collegii novi Aberdonensis (10 February 1722): Aberdeen University Library, MS 34 (only pages 1-6, 9, and 10, which ends in mid-sentence, survive from this manuscript); quoted and translated by Sageng, op. cit. note 2, 95-101.
156. Maclaurin, op. cit. note 6, 91-93; cf. Sageng, op. cit. note 2, 116.
157. Roger Emerson, 'Science and the Origins and Concerns of the Scottish Enlightenment', History of Science, Vol. 26 (1988), 333-66, at 342.
158. David J.P. Hare and William F. Scott, 'The Scottish Ministers'Widows' Fund of 1744', in A. Ian Dunlop (ed.), The Scottish Ministers' Widows' Fund, 1743-1993 (Edinburgh: St Andrew Press, 1992), 56-76. Compare also Maclaurin's letters to Robert Wallace (23 May 1743) and to Andrew Mitchell (24 May 1743), on his work for the Fund: Mills (ed.), op. cit. note 28, 105-08, 109-10.
159. Anon., 'The Second Paper of Memoirs of Mr MacLaurin beginning 1725' (Glasgow University Library MS Gen 1378/2): this letter from Wallace of 26 February 1744 has been copied in an 18th-century hand; the catalogue says 'Contains material not used by Patrick Murdoch in his account of Maclaurin's life'.
160. Murdoch, op. cit. note 6, xix.
161. For example, Mills (ed.), op. cit. note 28, 79, 87, 90, 96, 97, 105-10, 166, 172, 252-53, 255-56, 308-13, 314-21, 327-33, 338-39, 340-42, 370-72, 394-95, 404-09, 441-54.
162. Ibid., 340.
163. Maclaurin, op. cit. note 1, 727-28, 733-35, 735-42.
164. Murdoch, op. cit. note 6, xix.
165. Emerson, op. cit. note 2, 162.
166. Ibid., 164.
167. Emerson, op. cit. note 133, 354.
168. Emerson, op. cit. note 2, 178.
169. See, for instance, John R.R. Christie, 'The Origins and Development of the Scottish Scientific Community, 1680-1760', History of Science, Vol. 12 (June 1974), 122-41, esp. 127-34.
170. Larry Stewart, The Rise of Public Science: Rhetoric, Technology, and Natural Philosophy in Newtonian Britain, 1660-1750 (Cambridge: Cambridge University Press, 1992), 391. Examples of such influential Newtonians include John T. Desaguliers, John Harris, Humphry Ditton, Edmund Halley, Stephen Hales, Henry Beighton, Martin Triewald and John Horseley. Desaguliers was markedly influential as a populariser.
171. Amos Funkenstein, Theology and the Scientific Imagination (Princeton, NJ: Princeton University Press, 1986), 358: I owe this reference to Porter (1995), op. cit. note 3, 78.
172. Stewart, op. cit. note 146, 361.
173. Ibid., 392.
174. Porter (1992), op. cit. note 3, 647.
175. At Muirhouse, near Hamilton, in 1730: see the manuscript GUL MS Gen 1378/2, op. cit. note 135, 5.
176. As a measure of John Maclaurin's prominence in Scottish history, Thomas Reid's biographer Alexander Campbell Fraser, in order to identify Colin Maclaurin, calls him 'the brother of the eloquent Presbyterian preacher': A.C. Fraser, Thomas Reid (Edinburgh: Oliphant, 1898), 20.
177. Alexander Murdoch, The People Above: Politics and Administration in Mid-Eighteenth-Century Scotland (Edinburgh: John Donald, 1980), 2.
178. Ibid., 3.
179. Ibid., 6.
180. John Stuart Shaw, The Management of Scottish Society, 1707-1764 (Edinburgh: John Donald, 1983), 49.
181. The Argathelians had family ties to many peers, including Lothian, Sunderland, Lauderdale, Bute, Buccleuch, Loudun, Breadalbane, Crawford, Home, Moray, Caithness, Eglinton and Rosebery; the Duke of Argyll was also chief of the Campbell clan: Shaw, op. cit. note 156, 46. The Squadrone was essentially a family interest, including Montrose, Roxburghe, Tweeddale, Rothes, Haddington, Hopetoun, Marchmont (unusual in not having strong blood ties with the others), Findlater and Dundas: ibid., 48.
182. Murdoch, op. cit. note 153, 31.
183. Ibid., 7.
184. Shaw, op. cit. note 156, 46.
185. William Ferguson, Scotland: 1689 to the Present (Edinburgh: Oliver & Boyd, 1968), 147.
186. Shaw, op. cit. note 156, 130. Incidentally, the rival Bank of Scotland had been a Squadrone stronghold.
187. Roger Emerson, 'The "Affair" at Edinburgh and the "Project" at Glasgow: The Politics of Hume's Attempts to Become a Professor', in M.A. Stewart and John P. Wright (eds), Hume and Hume's Connections (University Park, PA: Pennsylvania State University Press, 1995), 1-22, at 1.
188. Ibid., 2.
189. Mills (ed.), op. cit. note 28, 32, 46, 60, 111-12, 171.
190. Ibid., 111: 'With him the Spirit & Honour of Scotland is gone . . . I never loved a great man so much, and I never had so much reason to think I had a real Share in the regard of such a man', Maclaurin wrote to Archibald Campbell of Knockbuy on 4 October 1743, the day of the Duke's death.
191. Mills (ed.), op. cit. note 28, 32.
192. Ibid., 32-33.
193. I thank Dr J.R.R. Christie for suggesting this possibility.
194. Scott, op. cit. note 32, 87, states: 'The excise board was basically Argathelian in sympathy throughout 1725-48'.
195. Scottish Record Office RH 2/4/446, 382; Scott, op. cit. note 32, 83.
196. Mills (ed.), op. cit. note 28, 11, 99, 163. Burnet was not in favour with Islay: see Scott, op. cit. note 32, 86.
197. Ibid., 84n.
198. Shaw, op. cit. note 156, 121-22.
199. Ibid., 65.
200. Scott, op. cit. note 32, 124.