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The calculating eye: Baily, Herschel, Babbage and the business of astronomy

  • William J. Ashworth (a1)
Extract

Astronomy does not often appear in the socio-political and economic history of nineteenthcentury Britain. Whereas contemporary literature, poetry and the visual arts made significant reference to the heavens, the more earthbound arena of finance seems an improbable place to encounter astronomical themes. This paper shows that astronomical practice was an important factor in the emergence of what can be described as an accountant's view of the world. I begin by exploring the senses of the term ‘calculation’ in Regency England, and then seek to reveal how the dramatic growth of vigilance in science, the organization and control of labour, and the monitoring of society and the economy drew upon and informed this disciplined numerical technique. Observations in all these areas could only be trusted if correctly reduced through a single system of calculation assisted by a group of standardized tables and division of mental labour. Within this setting the stellar economy provided an object that was seemingly ordered and law-like and therefore predictable through a powerful combination of techniques.

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I would like to thank Janet Browne, Boyd Hilton, Patrick O'Brien, Simon Schaffer and Andrew Warwick for their helpful suggestions. For permission to quote from manuscript materials I am grateful to the Royal Society, the Harry Ransom Humanities Center at the University of Texas at Austin, the Royal Astronomical Society, Cambridge University Library, St John's College, Cambridge, and the British Library.

1 Babbage, Charles, On the Economy of Machinery and Manufacturers, 4th edn, London, 1835, 387–8.

2 Bentham, Maria Sophia, Suggestions for the Better Management of the Civil Concerns of the Navy: Taken from the Papers of the Late Samuel Bentham, London, 1850, 49.

3 Sombart, Werner, Der Moderne Kapitalismus, 6th edn, Munich and Leipzig, 1924, ii, 119. Quoted in Studies in the History of Accounting (ed. Littleton, A. C. and Yamey, B. S.), London, 1956, 34.

4 Maunder, E. Walter, The Royal Observatory Greenwich: A Glance at its History and Work, London, 1900, 15.

5 Dodd, George, Days at the Factories, or The Manufacturing Industry of Great Britain Described, London, 1843, 548. Quoted in Berg, Maxine, The Machinery Question and the Making of Political Economy 1815–1848, Cambridge, 1980, 194.

6 Turner, H. H., ‘The decade 1820–1830’, in The History of the Royal Astronomical Society (ed. Dreyer, J. L. E. and Turner, H. H.), London, 1923, 149, on 2. Those also present were: two lawyers, Daniel Moore and Charles Stokes; Olinthus Gregory, professor of mathematics at Woolwich Royal Military Academy; Captain Thomas Colby of the Royal Engineers; Rev. William Pearson; James South, a rich amateur astronomer trained in medicine; and lastly, Peter Slawinski, a professor at Vilna University in Poland and from 1825 Director of the Vilna Observatory.

7 Quoted in Dyer, G. P., ‘“One of the Best Men of Business”: Master of the Royal Mint’, in John Herschel 1792–1871: A Bicentennial Commemoration (ed. King-Hele, D. G.), Proceedings of a Royal Society Meeting held on 13 May 1992, London, 1992, 105–13, on 105.

8 Turner, , op. cit. (6), 35.

9 Rudwick, M. J. S., ‘The foundation of the Geological Society of London: its scheme for co-operative research and its struggle for independence’, BJHS (1963), 4, 325–55, on 344–5.

10 Minutes of the Political Economy Club, 1821, in The Political Economy Club, London, 1921, vi, 1.

11 Baily, to Babbage, , 11 03 1820, Babbage correspondence, British Library.

12 Morus, Iwan, Schaffer, Simon and Secord, Jim, ‘Scientific London’, in London – World City 1800–1840 (ed. Fox, Celina), Recklinghausen, 1992, 129–42, on 129.

13 For this view see the official history of the Society given in Dreyer, and Turner, , op. cit. (6).

14 Herschel, John, ‘Address to the Society’, Memoirs of the Astronomical Society of London (1824), 1, 17, on 4.

15 Turner, , op. cit. (6), 25.

16 Baily, Francis, ‘On Mr. Babbage's new machine for calculating and printing mathematical and astronomical tables’, from H.Schumacher's ‘Astronomische Nachrichten’, 1823, no. 46, reprinted in the Philosophical Magazine (May 1824), and Babbage's Calculating Engines: A Collection of Papers by Henry Prevost Babbage (ed. Bromley, Allan G.), Los Angeles, 1982, 225–35, on 228 and 229.

17 Montgomery, James, The Theory and Practice of Cotton Spinning; or the Carding and Spinning Master's Assistant, Glasgow, 1833, 243. Quoted in Berg, , op. cit. (5), 193.

18 Baily, , op. cit. (16), 229–30.

19 Baily, to Babbage, , 8 11 1823, Babbage correspondence, British Library.

20 Berg, , op. cit. (5), see ch. 7.

21 Miller, David Philip, ‘The Royal Society of London 1800–1835: A Study in the Cultural Politics of Scientific Organization’, Ph.D thesis, University of Pennsylvania, 1981, 108–9. See also his ‘The revival of the physical sciences in Britain 1815–1840’, Osiris (1986), 2, 107–35. For the quote see Some Members in the Minority, An History of the Instances of Exclusion from the Royal Society, London, 1784, 20; and for Mutton's book-keeping see his A Complete Treatise on Practical Arithmetic and Bookkeeping, Both by Single and Double Entry, 14th edn, London, 1815.

22 Babbage, , op. cit. (1), 169.

23 Rosenberg, Nathan, ‘Adam Smith and moral capital’, History of Political Economy (1990), 1, 117.

24 Berg, , op. cit. (5), 160.

25 See Hoskin, Michael, ‘Astronomers at war: South versus Sheepshanks’, Journal of the History of Astronomy (1989), 20, 175212 and ‘More on South versus Sheepshanks’, Journal of the History of Astronomy (1991), 22, 174–9.

26 Robinson, Thomas Romney, Proceedings of the Royal Society (18671868), 16, pp. xlivxlvii, on xlvi. Quoted in Hoskin, , op. cit. (25), 183.

27 Babbage, , op. cit. (1), 379.

28 Baily, , op. cit. (16), 226.

29 Price, Richard, Observations on Reversionary Payments; on Schemes for Providing Annuities for Widows, and for Persons in Old Age; on the Method of Calculating the Values of Assurances on Lives; and on the National Debt, London, 1769, 131.

30 See Herschel, John, ‘Memoir of Francis Baily’, Monthly Notices of the Royal Astronomical Society (1844), 6, reprinted in his Essays from the Edinburgh and Quarterly Review, London, 1857, 552621. It was probably Baily's financial acumen that ensured the Society's financial status in its early years. Most of the compositions were invested in the Navy 5 per cents, while fees from non-resident members were invested in East India Bonds. These two sources of income were kept separate from the annual payments. See ‘Report of the Council of the Society to the First General Meeting’, 9 02 1821, Memoirs of the Astronomical Society (1824), 1, 2132, on 26.

31 Horton-Smith, L. G. H., ‘Francis Baily: The Astronomer 1774–1844’, The Newburian, Newbury, 1937, reprinted as a short pamphlet in 1938, 4.

32 Hilton, Boyd, Corn, Cash, Commerce: The Economic Policies of the Tory Governments, 1815–1830, Oxford, 1977; Brewer, John, ‘Commercialisation and politics’, in The Birth of a Consumer Society: The Commercialisation of Eighteenth-Century England (ed. McKendrick, N., Brewer, J. and Plumb, J. H.), London, 1982; and Perkin, Harold, The Origins of Modern Society, 1780–1880, London, 1969.

33 Baily, Francis, Tables for the Purchasing and Renewing of Leases, for Terms of years Certain and for Lives, with Rules for Determining the Value of the Reversion of Estates after any such Leases; and for the Solution of other Useful Problems; Adapted to General use, London, 1802, 8 and 37.

34 Hacking, Ian, The Taming of Chance, Cambridge, 1990, 49.

35 Baily, Francis, The Doctrine of Interest and Annuities Analytically Investigated and Explained Together with Several Useful Tables Connected with the Subject, London, 1808, pp. vvi.

36 Baily, , op. cit. (35), 105.

37 Baily, , op. cit. (35). The Sinking Fund was originally set up in the early eighteenth century to pay off the national debt. However, most governments did not use it for this purpose and in practice it had been used as a reserve fund in case of sudden need, i.e. war. It was abandoned in 1828.

38 Baily, , op. cit. (35), 6 and 106.

39 Milgate, Murray and Stimson, Shannon C., Ricardian Politics, Princeton, 1991, 75.

40 Baily, , op. cit. (35), 2nd edn, 1810, p. i. This edition is substantially different in detail and greatly extended.

41 Baily, , op. cit. (35), p. v.

42 Baily, , op. cit. (35), p. x.

43 Herschel, , op. cit. (30), 6; Charles Babbage, ‘On the influence of signs in mathematical reasoning’, a paper read to the Cambridge Philosophical Society on 16 December 1821 and printed in the Transactions of the Cambridge Philosophical Society (1827), 2, 325–77, on 373.

44 Baily, Francis, An Account of the Several Life Assurance Companies Established in London: Containing a View of their Respective Merits and Advantages, London, 1810, 12. Richard Price constructed the Northampton tables for this Society.

45 ‘Regulations of the Society’, Memoirs of the Astronomical Society (1824), 1, 912.

46 Herschel, , op. cit. (30), 8.

47 Sir George Colebrooke was head of the firm ‘Colebrooke, Lesingham and Binns’, Bankers of Threadneedle Street; the latter two were only nominal partners. Sir George was the son of James Colebrooke, a banker who had made a large fortune in the South Sea Bubble years. Sir George played an important part in the dealings and politics of the East India Company and was made their Chairman in 1769. His activities in the company were not thought by his enemies to be independent of his interests as a stockbroker. See Sutherland, Lucy, Politics and Finance in the Eighteenth Century (ed. Newman, Aubrey), London, 1984, 445–71.

48 Colebrooke, T. E., The Life of H. T. Colebrooke, 3 vols., London, 1873, i, 109.

49 Colebrooke, Henry, Remarks on the Present State of the Husbandry and Commerce of Bengal, Calcutta, 1795.

50 Colebrooke, H., op. cit. (49), 174.

51 Colebrooke, H., op. cit. (49), 94.

52 Colebrooke, Henry to Colebrooke, George, 28 07 1788. Quoted in Colebrooke, T. E., op. cit. (48), 31.

53 Colebrooke, T. E., op. cit. (48), 271–2.

54 Colebrooke, T. E., op. cit. (48), 296.

55 Colebrooke, T. E., op. cit. (48), 297.

56 See ‘Minutes of the Council of the Astronomical Society’, 9 03 1821, Royal Astronomical Society archives.

57 Gompertz won the annual prize, without exception, between 1812 and 1822 for the best solutions to prize questions contained in the Gentlemen's Mathematical Companion.

58 Adler, Marcus N., ‘Memoir of the late Benjamin Gompertz’, paper read before the Institute of Actuaries and of the Statistical Society, 18 12, 1865. Printed in The Assurance Magazine and the Institute of Actuaries (1867), 13, 120, on 1–2.

59 Adler, , op. cit. (58), 5.

60 Adler, , op. cit. (58), 16.

61 DNB, entry for Joshua Milne.

62 The Works of Charles Babbage (ed. Campbell-Kelly, Martin), London, 1989, iv, 1415.

63 Baily, , op. cit. (35), 60.

64 Gompertz's first paper to the Royal Society in 1806 was on the application of the method of differences to a species of series whose sums are obtained through impossible quantities. The paper was communicated through the then Astronomer Royal, Dr Maskelyne. See Adler, , op. cit. (58), 6. For Frend's rejection of negative and imaginary quantities see his Principles of Algebra, London, 1796.

65 Hacking, , op. cit. (34), 49.

66 Adler, , op. cit. (58), 16.

67 Babbage, , A Comparative View of the Various Institutions for the Assurance of Lives, London, 1826, 13.

68 Adler, , op. cit. (58), 1213.

69 De Morgan, Augustus, Athenaeum, 22 07 1865. Quoted in Adler, , op. cit. (58), 13.

70 Brown, Samuel, ‘President of the Institute of Actuaries, Extracts from the Opening Address of the President of Section F [Economics, Science and Statistics] of the BAAS, at the 38th Meeting at Norwich, August 1868’, The Assurance Magazine and the Institute of Actuaries (1870), 15, 19.

71 DNB, entry for Patrick Kelly.

72 Miller, ‘Royal Society’, op. cit. (21), 112.

73 Kelly, Patrick, The Universal Cambist, and Commercial Instruction; Being a General Treatise on Exchange, Including the Monies, Coins, Weights, and Measures, of all Trading Nations and Colonies, with an Account of Their Books and Paper Currencies, 2 vols., London, 1811, i, p. i. For Kelly's book-keeping see his The Elements of Book-Keeping both by Single and Double Entry, London, 1801.

74 Kelly, , Universal Cambist, op. cit. (73), p. ii.

75 Kelly, , Universal Cambist, op. cit. (73), p. xxi.

76 Kelly, , Universal Cambist, op. cit. (73), p. xxiv. Paper credit included Bank notes, Exchequer, Navy and Ordinance Bills, Bonds, Mortgages, Transfers of Stock, Bills of Exchange and all other forms of paper securities.

77 Clerke, Agnes M., A Popular History of Astronomy During the Nineteenth Century, London, 4th edn, 1908, 7.

78 Schaffer, Simon, ‘Herschel in bedlam: natural history and stellar astronomy’, BJHS (1980), 13, 211–39 and ‘Uranus and the establishment of Herschel's astronomy’, Journal for the History of Astronomy (1981), 12, 1126; Williams, M. E., ‘Was there such a thing as stellar astronomy in the eighteenth century?’, History of Science (1983), 21, 369–85.

79 Dewhirst, David W., ‘Meridian astronomy in the private and university observatories of the United Kingdom: rise and fall’, Vistas in Astronomy (1985), 28, 147–58, on 147.

80 Herschel, John, A Preliminary Discourse on the Study of Natural Philosophy (1830), Chicago, 1987, 276.

81 Herschel, , op. cit. (80), 280.

82 Desmond, Adrian, The Politics of Evolution: Morphology, Medicine and Reform in Radical London, Chicago, 1989. For astronomy see Schaffer, Simon, ‘The nebular hypothesis and the science of progress’, in History, Humanity and Evolution: Essays in Honour of John C. Greene (ed. Moore, J. R.), Cambridge, 1989, 131–64.

83 Hoppit, Julian, Risk and Failure in English Business 1700–1800, Cambridge, 1987, 166.

84 Hilton, Boyd, The Age of Atonement: The Influence of Evangelicalism on Social and Economic Thought 1785–1865, Oxford, 1988, 123 and 140.

85 For an analysis of the prevalent balanced and atemporal view of the world in the early nineteenth century see Hilton, , op. cit. (84), especially ch. 8, and M. Norton Wise with the collaboration of Smith, Crosbie, ‘Work and waste: political economy and natural philosophy in nineteenth century Britain (I)’, History of Science (1989), 27, 262301, ‘Work and waste (II)’, History of Science (1989), 27, 391449, and ‘Work and waste (III)’, History of Science (1990), 28, 221–56. The change from a static to a dynamical view roughly occurs during the 1830s.

86 Hoppit, , op. cit. (83), 172 and 39. See also Yamey, B. S., ‘Scientific bookkeeping and the rise of capitalism’, Economic History Review (1949), 2nd series, 1, 99114.

87 Hoppit, , op. cit. (83).

88 Scrope, George Poulett, On Credit Currency and its Superiority to Coin, London, 1830, 74.

89 Ricardo, David, Principles of Political Economy and Taxation, 3rd edn, London, 1821. Everyman reprint, 1926, 50.

90 Hilton, , op. cit. (32), 179.

91 Colebrooke, H., op. cit. (49), 279.

92 David Ricardo quoted by his fellow club member Mallet, J. L., op. cit. (10), p. x.

93 Thompson, E. P., ‘Time-discipline, and industrial capitalism’, Past and Present (12 1967), 5697.

94 Herschel, John, ‘Elements of Greatness’, Herschel MS, n.d. Harry Ransom Humanities Research Centre, University of Texas at Austin.

95 Herschel, , op. cit. (80), 27.

96 Quoted in Schaffer, , op. cit. (82), 135.

97 Wise, with Smith, , op. cit. (85), I, 277.

98 Taylor, William Cooke, Factories and the Factory System, London, 1844, p. iii.

99 Cariyle, Thomas, ‘Signs of the times’, Edinburgh Review (06 1829), reprinted in A Cariyle Reader: Selections from the Writings of Thomas Cariyle (ed. Tennyson, G. B.), Cambridge, 1984, 3154, on 46.

100 Farr, William, ‘On the construction of Life Tables, illustrated by a new Life Table of the healthy districts of England’, The Assurance Magazine and the Institute of Actuaries (1861), 9, 121–2.

101 ‘Minutes of the Council of the Astronomical Society’, 9 03 1821, Royal Astronomical Society archives.

102 Brewer, John, The Sinews of Power: War, Money and the English State, 1688–1783, London, 1989, 67–9.

103 Brewer, , op. cit. (102), 94 and 92.

104 Brewer, , op. cit. (102), 84.

105 Hacking, , op. cit. (34).

106 Meadows, A. J., Greenwich Observatory: Recent History (1836–1975), London, 1975, ii, 3.

107 In 1857 Airy wrote in his Report to the Board of Visitors: ‘The meridional system is sacredly preserved.’ Quoted in Meadows, , op. cit. (106), 4.

108 Schaffer, Simon, ‘Astronomers mark time: discipline and the personal equation’, Science in Context (1988), 2, 115–45.

109 Douglas, Mary, How Institutions Think, Syracuse, 1986, 1.

110 Miller, , op. cit. (21).

111 Rankin, Robert, A Familiar Treatise on Life Assurances and Annuities, London, 1830, 72.

112 Senior, Nassau William, An Outline of the Science of Political Economy, London, 1836, 135.

113 Senior, , op. cit. (112), 134.

114 Wise, with Smith, , op. cit. (85), II, 414.

115 Herschel, , op. cit. (30), 41.

116 Herschel, , op. cit. (30), 31; see also Pannekoek, A., A History of Astronomy, London, 1961, 321–38.

117 Herschel, John, ‘Address to the Astronomical Society of London’, 1829, in his Essays, op. cit. (30), 510.

118 Meadows, , op. cit. (106), 30.

119 Quoted in Meadows, , op. cit. (106), 29.

120 Berg, , op. cit. (5), 46.

121 Wise, with Smith, , op. cit. (85), I, 276.

122 Portlock, Colonel J. E., Memoir of the Life of Major General Colby, London, 1869, 8.

123 Quoted in Miller, , op. cit. (21), 321.

124 Turner, , op. cit. (6), 29.

125 Francis Baily, Notes and Appendix to Cagnoli, A., Memoir on a New and Certain Method of Ascertaining the Figure of the Earth, By Means of Occultations of the Fixed Stars, London, 1819, 31.

126 Baily, , op. cit. (125), 33–4.

127 Baily, Francis, Remarks on the Present Defective State of the Nautical Almanac, London, 1822, 18.

128 Baily, , op. cit. (127), 18.

129 Herschel, John, On the Board of Longitude, n.d. (1825?), Herschel MS, St John's College, Cambridge, my italics.

130 Baily, , op. cit. (127), 3943.

131 Herschel, John and Babbage, Charles, Memoirs of the Analytical Society, 1813, original manuscript, 12, Herschel MS, St John's College, Cambridge.

132 Charles Babbage, ‘On Transcendents’, Babbage MS, Cambridge University Library, probably 1812.

133 Baily, , op. cit. (16), 226.

134 This problem was international, tables were not reduced through standardized techniques and tools. See, for example, ‘On the Differences of Declination of Certain Stars, according to Different Astronomers; and on Refraction, &c. Extracted from a Letter of M. J. J. Littrow, Director of the Imperial Observatory at Vienna, to the Foreign Secretary’ – dated Vienna, 3 January 1823, Memoirs of the Astronomical Society (1824), 1, 339–48.

135 Baily, , op. cit. (127), 49.

136 South, James, ‘An inquiry how far it would be advisable that the daily corrections in right ascension and north polar distance of the forty-six zero stars should be computed annually at the public expense’, Annals of Philosophy (1824), January and February, printed as a separate pamphlet, London, 1824, 9.

137 Baily, , op. cit. (127), 60. See also Herschel, , op. cit. (129).

138 Herschel, , op. cit. (30), 19 (my italics).

139 Miller, , op. cit. (21), 324.

140 Herschel, John to Gurney, Hudson, MP, 25 06 1830, quoted from Schweber, S. S., Aspects of the Life of John Herschel, New York, 1981.

141 Herschel, John to SirWatson, William, 12 02 1819, Herschel correspondence, Royal Society.

142 Herschel, to Gurney, , op. cit. (140).

143 Herschel, , op. cit. (129).

144 Dickens, Charles, Hard Times (1850), Harmondsworth, 1985, 149–50.

145 Warwick, Andrew, ‘The Laboratory of Theory or What's Exact about the Exact Sciences?’, paper presented in Oldenburg, 08 1992.

146 Latour, Bruno, Science in Action: How to Follow Scientists and Engineers Through Society, Cambridge, Mass., 1987, ch. 6.

147 Quoted in Rosenberg, , op. cit. (23), 11.

148 Smith, Adam, ‘Essay on the history of astronomy’, in The Essays of Adam Smith: Philosophical and Literary (ed. Joseph Black and James Hutton), n.d., 325–85, on 352.

149 Bentham, Samuel, Naval Essays, or Essays on the Management of Public Concerns as Exemplified in the Naval Department, Considered as a Branch of the Business of Warfare, London, 1828, 9.

150 Bentham, , op. cit. (149), 36.

151 Bentham, Maria Sophia, The Life of Brigadier-General Sir Samuel Bentham, London, 1862, 98; Cooper, Carolyn C., ‘The Portsmouth system of manufacture’, Technology and Culture (1984), 2, 182226, on 192–206.

152 Bentham, M. S., op. cit. (151), 83.

153 Morriss, Roger, The Royal Dockyards During the Revolutionary and Napoleonic Wars, Leicester, 1983, especially ch. 7.

154 Bentham, M. S., op. cit. (151), 60.

155 Bentham, Jeremy, Panopticon; or, The Inspection House: Containing the Idea of a new Principle of Construction Applicable to any sort of Establishment …in a Series of Letters Written in the Year 1787, from Crecheff in White Russia, to a Friend in England, London, 1791, 23 and 107.

156 Bowring, John, The Works of Jeremy Bentham, Edinburgh, 1843, x, 226, quoted in Cooper, , op. cit. (151), 193.

157 Bentham, J., op. cit. (155), 45.

158 Herschel MS, n.d., Harry Ransom Humanities Research Center, University of Texas at Austin.

159 Berg, , op. cit. (5), 193.

160 See, for example, Baily, , op. cit. (44), Babbage, , op. cit. (67), Rankin, , op. cit. (111), Scrope, , op. cit. (88), and Bentham, Samuel, Financial Reform Scrutinized in a Letter to Sir Henry Parnell, Bart MP, London, 1830.

161 Berg, Maxine and Hudson, Pat, ‘Rehabilitating the Industrial Revolution’, Economic History Review (1992), 45, 2450, on 42.

162 Herschel, John, ‘Address to the Astronomical Society’, 11 04 1827, in his Essays, op. cit. (30), 466–88, on 470.

163 Quoted in Meadows, , op. cit. (106), 31.

164 Scrope, , op. cit. (88), 43–4; Milne, Joshua, Treatise on the Valuation of Annuities and Assurances on the Construction of Mortality, London, 1815, pp. 1 and xlii; A Gentleman of the Exchange, Stock-Exchange Laid Open, London, 1814, 26–7.

165 Michael Foucault uses panopticism as the paradigmatic characteristic of a prevalent disciplinary technology. See his, Discipline and Punish: The Birth of the Prison, London, 1977.

166 Bentham, Jeremy, Panopticon: Postscript; Part II: Containing a Plan of Management for a Panopticon Penitentiary House, London, 1791, 40.

167 Schaffer, , op. cit. (108), 118.

168 Babbage, , op. cit. (1), 367.

169 Babbage, , op. cit. (1), 169.

170 Cooper, , op. cit. (151), 193.

171 Babbage, , op. cit. (1), 201.

172 Bessel quoted in Littrow, , op. cit. (134), 343.

173 Quoted in Pannekoek, , op. cit. (116), 325.

174 Littrow, , op. cit. (134), 342.

175 Gompertz, Benjamin, ‘On the theory of astronomical instruments, Part 1’, Memoirs of the Astronomical Society (1824), 1, 349–55, on 349.

176 Gompertz, , op. cit. (175).

177 Baily, , op. cit. (16), 229.

178 See Bennett, Jim, ‘Instrument makers and the “Decline of Science in England”: the effects of institutional change on the elite makers of the early nineteenth century’, in Nineteenth-Century Scientific Instruments and Their Makers (ed. de Clerq, P. R.), Amsterdam, 1985, 1329.

179 Berg, , op. cit. (5), 33.

180 Herschel, John, ‘Address to the Astronomical Society’, 11 04 1827, in Essays op. cit. (30), 466–88, on 483–4.

181 Herschel, John, ‘Address to the B.A.A.S. at Cambridge’, 19 06 1845, in Essays op. cit. (30), 655.

182 Babbage, , op. cit. (1), 379.

183 Baily, , op. cit. (16), 225.

184 Quoted in Berg, , op. cit. (5), 128.

185 Colebrooke, Henry, ‘On presenting the honorary medals of the Society’, Memoirs of the Astronomical Society (1824), 1, 509–14, on 509.

186 Miller, , ‘Royal Society’, op. cit. (21), 217.

187 Review of ‘Letters addressed to H. R. H. the Grand Duke of Saxe-Coburg and Gotha, on the theory of probabilities as applied to the moral and political sciences, by M. A. Quetelet, Astronomer Royal of Belgium, translated by Olinthus Gregory Downes, London, 1849’, The Assurance Magazine and the Institute of Actuaries (1851), 1, 362.

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