A "large and graceful sinuosity": John Herschel's graphical method

ISIS

Volumn 97, Issue 4, 2006, Pages 605-633

  Hankins, Thomas L ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ASTRONOMY; HISTORY; HUMAN; MATHEMATICS; PHYSICS; STATISTICAL ANALYSIS;

ASTRONOMY; DATA INTERPRETATION, STATISTICAL; HISTORY, 19TH CENTURY; HUMANS; MATHEMATICS; PHYSICS;

EID: 33847316976     PISSN: 00211753     EISSN: 15456994     Source Type: Journal    
DOI: 10.1086/509946     Document Type: Article

References (128)

1. John F. W. Herschel, "Quetelet on Probabilities" (1850), in Essays from the Edinburgh and Quarterly Reviews (London: Longman, Brown, Green, Longmans & Roberts, 1857; rpt., New York: Arno, 1981) (hereafter cited as Essays), pp. 365-465, on p. 452.
2. The word "graph" was first used by J. J. Sylvester in 1878; therefore the use of the term in this essay is anachronistic. However, it is the term we commonly use today for a diagram relating measured physical quantities by a curve, and so I have employed it, although a contemporary would have used "curve," "diagram," "Figur," "graphique," or "arithmétique linéaire." See Thomas L. Hankins, "Blood, Dirt, and Nomograms: A Particular History of Graphs," Isis, 1999, 90:50-80, esp. 52-54.
3. On the origins of graphs see Laura Tilling, "Early Experimental Graphs," British Journal for the History of Science, 1975, 8:193-213;
4. James Beniger and Dorothy L. Robyn, "Quantitative Graphics in Statistics: A Brief History," American Statistician, Feb. 1978, 32(1):1-11;
5. H. G. Funkhouser, "Historical Development of the Graphical Representation of Statistical Data," Osiris, 1st Ser., 1937, 3:269-404;
6. and Howard Wainer, Graphic Discovery: A Trout in the Milk and Other Visual Adventures (Princeton, N.J.: Princeton Univ. Press, 2005), Pt. 1.
7. John F. W. Herschel, "On the Investigation of the Orbits of Revolving Double Stars: Being a Supplement to a Paper Entitled 'Micrometrical Measures of 364 Double Stars &c, &c,'" Memoirs of the Royal Astronomical Society, 1833, 5:171-222 (read 13 Jan. 1832);
8. and William Herschel, "Account of the Changes That Happened during the Last Twenty-five Years in the Relative Situation of Double-Stars: With an Investigation of the Cause to Which They Are Owing," Philosophical Transactions of the Royal Society, 1803, 93:339-382, 1804, 94:353-384, esp. 1803, 93:340.
9. Felix Savary, "Sur la détermination des orbites qui décrivent autour de leur centre de gravité deux étoiles très rapprochées l'une de l'autre," in Bureau des Longitudes, Connaissance des temps ou des mouvements célestes, à l'usage des astronomes et des navigateurs (Paris: Gauthier-Villars, 1830), pp. 56-69;
10. Savary, "Addition à la note sur le mouvement des étoiles doubles," ibid., pp. 163-171;
11. and Johann Franz Encke, "Über die Berechnung der Bahnen der Doppelsterne," in Astronomischen Recheninstitut der deutschen Akademie der Wissenschaften zu Berlin, Berliner astronomische Jahrbuch (Berlin: Akademie Verlag, 1832), pp. 253-304.
12. On the gentleman astronomers see Allan Chapman, "An Occupation for an Independent Gentleman: Astronomy in the Life of John Herschel," Vistas in Astronomy, 1993, 36:71-116, esp. pp. 72-73;
13. and Henry C. King, The History of the Telescope (New York: Dover, 1979), pp. 192-194, 200-203.
14. John F. W. Herschel, Observations Made during the Years 1834, 5, 6, 7, 8 at the Cape of Good Hope: Being the Completion of a Telescopic Survey of the Whole Surface of the Visible Heavens, Commenced in 1825 by Sir J. F. W. Herschel (London: Smith & Elder, 1847) (hereafter cited as Cape Results), p. 165.
15. Michael A. Hoskin, "John Herschel and Astronomy: A Bicentennial Appraisal," from The John Herschel Bicentennial Symposium Held in Herschel School, Claremont, 6 March 1992, ed. B. Warner (Cape Town: Royal Society of South Africa, 1992), pp. 1-17, esp. p. 6.
16. Bessel announced his results in a letter to Herschel: Friedrich Wilhelm Bessel to J. F. W. Herschel, 9 Oct. 1838, Herschel Papers, Royal Society of London (hereafter cited as Herschel Papers), 4.71.
17. See also Herschel, "Address of the President, Sir J. F. W. Herschel, Bart., on the Presentation of the Gold Medal of the Royal Astronomical Society to Professor Bessel, at the Anniversary Meeting, February 12, 1841, for His Observations and Researches on the Parallax of 61 Cygni," in Essays, pp. 532-551.
18. On the history of the search for stellar parallax see Mari Elen Wyn Williams, "Attempts to Measure Annual Stellar Parallax: Hooke to Bessel" (Ph.D. diss., Imperial College London, 1981), Ch. 6, esp. pp. 175-176;
19. and Alan W. Hirshfeld, Parallax: The Race to Measure the Cosmos (New York: Freeman, 2001), Ch. 16.
20. The star with the greatest parallax, α Centauri, is visible only from the Southern Hemisphere. Herschel could easily have detected the parallax of this star if he had searched for it while he was at the Cape. The Cape Astronomer, Thomas Henderson, had obtained the necessary data just before Herschel's arrival but hesitated to publish his results. Herschel gave him credit for being the first to detect parallax, although Bessel's data were more convincing. See Herschel, "Address on the Presentation to Bessel," pp. 546-549;
21. and Hirshfeld, Parallax, pp. 201-205.
22. John Herschel defended reflecting telescopes against Fraunhofer's claim for the superiority of refractors in "Observations on Mr. Fraunhofer's Memoir on the Inferiority of Reflecting Telescopes When Compared with Refractors," Quarterly Journal of Science, 1826, 20:288-293.
23. Herschel, "On the Investigation of the Orbits of Revolving Double Stars" (cit. n. 3), p. 178.
24. On the history of graph paper see William H. Brock and Michael H. Price, "Squared Paper in the Nineteenth Century: Instrument of Science and Engineering and Symbol of Reform in Mathematical Education," Educational Studies in Mathematics, 1980, 11:365-381.
25. Squared paper was used as early as the seventeenth century for laying out ship designs, but not for plotting data; see Wainer, Graphic Discovery (cit. n. 2), p. 11.
26. John F. W. Herschel, Outlines of Astronomy, new ed. (London: Longmans, Green, 1875), p. 77.
27. Herschel had already argued the advantage of using the position angles of optical doubles to detect parallax: John F. W. Herschel, "On the Parallax of the Fixed Stars," Phil. Trans. Roy. Soc., 1826, 116:266-280.
28. On the parallel-thread revolving micrometer see Herschel, Cape Results, p. 245.
29. According to Kepler's second law, sectors of the ellipse swept out in equal times by the radius vector will have equal areas. For short times the sectors may be approximated by triangles with bases equal to the radius vectors and heights equal to the products of the radius vectors, the angular velocities, and the times. The times are taken to be equal for all the sectors, so the radius vectors are inversely proportional to the square roots of the angular velocities.
30. Herschel, "On the Investigation of the Orbits of Revolving Double Stars" (cit. n. 3), pp. 179, 181.
31. Howard Wainer cites Herschel's diagram as one of the first, if not the first, scatter plots: Wainer, Graphic Discovery (cit. n. 2), p. 24.
32. Herschel, "On the Investigation of the Orbits of Revolving Double Stars," p. 192.
33. Ibid., p. 183.
34. Ibid., p. 194;
35. and Herschel, Outlines of Astronomy (cit. n. 10), p. 616.
36. William Henry Smyth, A Cycle of Celestial Objects (London, 1844), p. 292,
37. quoted in Chapman, "Occupation for an Independent Gentleman" (cit. n. 4), p. 82;
38. and Herschel, "On the Investigation of the Orbits of Revolving Double Stars," pp. 210-211 (on Savary), 212, 218 (on Encke).
39. Johann Franz Encke to Herschel, 8 Sept. 1833, and Herschel to Encke, 17 Jan. 1837: Herschel Papers, 7.89, 25.5.5. Herschel told Encke that the appointment of George Biddell Airy as Astronomer Royal at Greenwich Observatory marked an improvement in the professionalism of British astronomers; I thank Michael J. Crowe for providing me with a copy of this letter.
40. Herschel to Augustus De Morgan, 26 Mar. 1849, Herschel Papers, 23.63; A. J. F. Yvon Villarceau to Herschel, 1 Apr. 1849, Herschel Papers, 17.418; Herschel to George Biddell Airy, 9 Apr. 1849, Archives of the Royal Greenwich Observatory, 6.231.176; rand Herschel to Villarceau, 19 Apr. 1849, Herschel Papers, 17.41a.
41. The letters are abstracted in John Frederick William Herschel, A Calendar of the Correspondence of Sir John Herschel, ed. Michael J. Crowe (Cambridge: Cambridge Univ. Press, 1998), item nos. 8012, 8022, 8030, 8036.
42. John F. W. Herschel, "On the Determination of the Most Probable Orbit of a Binary Star," Mem. Roy. Astron. Soc., 1849, 18:47-68, on p. 47.
43. Herschel submitted his article in two parts, on 26 and 27 Mar. 1849, for publication in the Memoirs of the Royal Astronomical Society and sent a letter on 19 Mar. 1849 to Urbain J. J. Leverrier for publication in the Comptes Rendus of the Paris academy: "Extrait d'une lettre à M. Le Verrier sur sa méthode pour la détermination de l'orbite des étoiles doubles," Comptes Rendus de l'Académie des Sciences, 1849, 28:421-422.
44. See also Mari Williams, "Beyond the Planets: Early Nineteenth-Century Studies of Double Stars," Brit. J. Hist. Sci., 1984, 17:295-309, esp. p. 309.
45. Herschel, "On the Determination of the Most Probable Orbit of a Binary Star," p. 68. Although the method of least squares was universally used during the nineteenth century, there was still debate over its validity.
46. See Mansfield Merriman, "A List of Writings Relating to the Method of Least Squares, with Historical and Critical Notes," Transactions of the Connecticut Academy of Arts and Sciences, 1877-1992, 4:151-232.
47. William Whewell, The Philosophy of the Inductive Sciences, Founded upon Their History (1840), facsimile of the second edition (Sources of Science, 41), 2 vols. (New York: Johnson Reprint, 1967), Vol. 2, p. 395.
48. Whewell, Philosophy of the Inductive Sciences, Vol. 2, pp. 396-397.
49. William Whewell, The Mechanical Euclid, Containing the Elements of Mechanics and Hydrostatics (Cambridge, 1837), p. 178,
50. quoted in Richard Yeo, Defining Science: William Whewell, Natural Knowledge, and Public Debate in Early Victorian Britain (Cambridge: Cambridge Univ. Press, 1993), p. 161.
51. Whewell, Philosophy of the Inductive Sciences (cit. n. 23), Vol. 2, pp. 398, 399;
52. and John F. W. Herschel, "Whewell on the Inductive Sciences," in Essays, pp. 142-256, on p. 249.
53. do not know why this distinction was not stated more clearly. In his review of the work containing Adolphe Quetelet's famous study of "Scottish chests" Herschel recognized the difference. Quetelet had shown that the chest measurements of Scottish soldiers followed a normal distribution. He suggested that an individual making repeated measurements of a single chest, if he were a poor enough measurer, might obtain the same normal distribution as an accurate measurer of many chests. In the first case the distribution was random error in the measurements; in the second case it was random variation in actual chests. Herschel pointed out that any measurer was unlikely to be so incompetent that he would make a mistake of the magnitude covered by the variation in actual chests. Herschel, "Quetelet on Probabilities" (cit. n. 1), p. 407.
54. Herschel accused Whewell of improperly excluding mathematics from his History of the Inductive Sciences: Herschel, "Whewell on the Inductive Sciences" (cit. n. 26), p. 189.
55. On Herschel's scientific method see Marvin Paul Bolt, "John Herschel's Natural Philosophy: On the Knowing of Nature and the Nature of Knowing in Early-Nineteenth-Century Britain" (Ph.D. diss., Univ. Notre Dame, 1998);
56. Richard Yeo, "Reviewing Herschel's Discourse," Studies in History and Philosophy of Science, 1989, 20:541-552;
57. Joseph Agassi, "Sir John Herschel's Philosophy of Success," Historical Studies in the Physical Sciences, 1969, 1:1-36;
58. Arthur Fine, "Foreword," in John F. W. Herschel, A Preliminary Discourse on the Study of Natural Philosophy, facsimile of the 1830 edition (Chicago: Univ. Chicago Press, 1987), pp. v-xxi;
59. Curt Ducasse, "John F. Herschel's Method of Inquiry," in Theories of Scientific Method: The Renaissance through the Nineteenth Century, ed. Edward H. Madden (Seattle: Univ. Washington Press, 1966), pp. 153-182;
60. and David Wilson, "Herschel and Whewell's Version of Newtonianism," Journal of the History of Ideas, 1974, 35:79-97.
61. Herschel, "Whewell on the Inductive Sciences," p. 151.
62. Ibid., p. 246.
63. Ibid., p. 249.
64. John F. W. Herschel, "An Address to the British Association for the Advancement of Science at the Opening of Their Meeting at Cambridge, June 19th, 1845," in Essays, pp. 634-682, on p. 670;
65. and Yeo, "Reviewing Herschel's Díscourse" (cit. n. 28), p. 543.
66. William Whewell, History of the Inductive Sciences, 3rd ed., 3 vols. (London, 1857), Vol. 3, p. 55.
67. For the "Humboldtian" character of Herschel's Cape expedition see Steven Ruskin, John Herschel's Cape Voyage: Private Science, Public Imagination, and the Ambitions of Empire (Aldershot, Hants: Ashgate, 2004), pp. 12-36.
68. Herschel found the collection of meteorological data very demanding. See David S. Evans, Terence J. Deeming, Betty Hall Evans, and Stephen Goldfarb, eds., Herschel at the Cape: Diaries and Correspondence of Sir John Herschel, 1834-1838 (Austin: Univ. Texas Press, 1969), pp. 173-174;
69. and D. S. Evans, "Dashing and Dutiful," Science, N.S., 25 Apr. 1958, 127:935-948, esp. pp. 941-942.
70. On the establishment of meteorology in England see Katharine Anderson, Predicting the Weather: Victorians and the Science of Meteorology (Chicago: Univ. Chicago Press, 2005).
71. On Sabine see Nathan Reingold, "Edward Sabine," in Dictionary of Scientific Biography, ed. Charles C. Gillispie, 14 vols. (New York: Scribners, 1970-1980), Vol. 12, pp. 49-53.
72. On the magnetic crusade see John Cawood, "Terrestrial Magnetism and the Development of International Collaboration in the Early Nineteenth Century," Annals of Science, 1977, 34:551-587;
73. and Cawood, "The Magnetic Crusade: Science and Politics in Early Victorian Britain," Isis, 1979, 70:492-519.
74. For a detailed account of the politics that led to the British effort see Jack Morrell and Arnold Thackray, Gentlemen of Science: Early Years of the British Association for the Advancement of Science (Oxford: Clarendon, 1981), pp. 353-370.
75. In 1826 Herschel and Charles Babbage suggested that atmospheric electricity generated by thermoelectric action between earth and sky might be responsible for the earth's magnetism; see Cawood, "Magnetic Crusade," p. 497. Gauss sent a copy of his Allgemeine Theorie des Erdmagnetismus to Herschel on 7 May 1839: Herschel Papers, 8.77.
76. In 1838 Herschel delivered the Copley Medal awarded by the Royal Society to Gauss; see Cawood, "Magnetic Crusade," pp. 507-508.
77. Susan Faye Cannon, Science in Culture: The Early Victorian Period (New York: Dawson/Science History Publications, 1978), p. 104;
78. and Alexander von Humboldt, "Sur les lignes isothermes," Annales de Chimie et de Physique, 1817, 5:102-112.
79. See also Nicolaas Rupke, "Humboldtian Distribution Maps: The Spatial Ordering of Scientific Knowledge," in The Structure of Knowledge: Classifications of Science and Learning since the Renaissance, ed. Tore Frängsmyr (Berkeley: Office for History of Science and Technology, Univ. California, 2001), pp. 93-116, esp. p. 103;
80. Michael Dettelbach, "Global Physics and Aesthetic Empire: Humboldt's Physical Portrait of the Tropics," in Visions of Empire, ed. David Philip Miller and Peter Hanns Reill (Cambridge: Cambridge Univ. Press, 1996), pp. 258-292;
81. and Dettelbach, "Humboldtian Science," in Cultures of Natural History, ed. Nicholas Jardine, James A. Secord, and Emma Spary (Cambridge: Cambridge Univ. Press, 1996), pp. 287-304.
82. John F. W. Herschel, "Terrestrial Magnetism," Quarterly Review, June 1840, no. 131, in Essays, pp. 63-141, on p. 82.
83. Ibid., p. 89.
84. Herschel to William Whewell, 7 Aug. 1839, quoted in Morrell and Thackray, Gentlemen of Science (cit. n. 35), p. 360;
85. and Cawood, "Magnetic Crusade" (cit. n. 35), pp. 514-515.
86. Herschel directed the preparation of two manuals for the collection of geophysical measurements. The first was the Royal Society Report of the Committee of Physics, Including Meteorology, on the Objects of Scientific Inquiry in Those Sciences (London: Taylor, 1840), put together by a committee that Herschel chaired. The report contained desiderata for the upcoming Admiralty expedition of Captain James Clark Ross to Antarctica. It also contained forms and explicit instructions for the worldwide Magnetic and Meteorological Survey. Among the five journal books required for the survey was the "Curve Book." All the measurements were to be reduced and plotted as curves.
87. Herschel also edited the Admiralty Manual of Scientific Enquiry: Prepared for the Use of Her Majesty's Navy, and Adapted for Travellers in General (London: Murray, 1849), which ran through five editions and also frequently directed those collecting the data to plot them in curves.
88. Herschel, "Terrestrial Magnetism" (cit. n. 39), pp. 89-90.
89. John Michell, "An Inquiry into the Probable Parallax and Magnitude of the Fixed Stars from the Quantity of Light Which They Afford to Us, and the Particular Circumstances of Their Situation," Phil. Trans. Roy. Soc., 1767, 57:234-264;
90. and Herschel, Outlines of Astronomy (cit. n. 10), p. 607.
91. James David Forbes, "On the Alleged Evidence for a Physical Connexion between Stars Forming Binary or Multiple Groups, Arising from Their Proximity Alone," Philosophical Magazine, 3rd Ser., 1849, 35:132-133.
92. Herschel replied in "Quetelet on Probabilities" (cit. n. 1), pp. 427-430.
93. Forbes followed his letter with a longer article: "On the Alleged Evidence for a Physical Connexion between Stars Forming Binary or Multiple Groups, Deduced from the Doctrine of Chances," Phil. Mag., 3rd Ser., 1850, 37:401-427.
94. On this debate see Barry Gower, "Astronomy and Probability: Forbes versus Michell on the Distribution of the Stars," Ann. Sci., 1982, 39:145-160;
95. and Theodore M. Porter, The Rise of Statistical Thinking, 1820-1900 (Princeton, N.J.: Princeton Univ. Press, 1986), pp. 79-80.
96. Forbes, "On the Alleged Evidence for a Physical Connexion" (1850), p. 416.
97. G. B. Airy to J. D. Forbes, 11 Oct. 1850, in John Campbell Shairp, Peter Guthrie Tait, and A. Adams-Reilly, Life and Letters of James David Forbes, F.R.S. (London: Macmillan, 1873), pp. 476-477;
98. William Thomson to Forbes, 15 Aug. 1850, ibid., pp. 473-475, on p. 475;
99. and R. Leslie Ellis to Forbes, 3 Sept. 1850, 8 Oct. 1850, 10 Oct. 1850, ibid., pp. 479-493, on p. 490.
100. Ellis was a Fellow of Trinity College at Cambridge and founder, with D. F. Gregory, of the Cambridge Mathematical Journal. In 1849 he published "On the Foundations of the Theory of Probabilities," Transactions of the Philosophical Society of Cambridge, 1849, 8:1-6, in which he criticized the classical interpretation of probability theory.
101. Herschel, Preliminary Discourse on the Study of Natural Philosophy (cit. n. 28), p. 219.
102. For the 1850 treatment see Herschel, "Quetelet on Probabilities (cit. n. 1), pp. 398-400;
103. the simple derivation of the normal or Gaussian curve of errors became known as "Herschel's proof." See Merriman, "List of Writings Relating to the Method of Least Squares" (cit. n. 22), pp. 164, 192;
104. and J. W. L. Glaisher, "On the Law of Facility of Errors of Observations, and on the Method of Least Squares," Mem. Roy. Astron. Soc., 1871-1872, 39, Pt. 2, pp. 75-124, esp. pp. 112-116.
105. For Herschel on target shooting see Robin L. Plackett, "Herschel on Estimation," Journal of the Royal Statistical Society, Ser. A, 1992, 155, Pt. 1, pp. 29-35.
106. Herschel, "Quetelet on Probabilities," p. 429.
107. The debate was essentially settled by George Boole, who sided with Forbes; see Boole, "On the Theory of probabilities, and in Particular on Michell's Problem of the Distribution of Fixed Stars," Phil. Mag., 4th Ser., 1851, 1, rpt. in Boole, Studies in Logic and Probability, ed. R. Rhees (London: Watts, 1952), pp. 247-259.
108. John Herschel, "On the Estimation of Skill in Target Shooting," in Familiar Lectures on Scientific Subjects (1867; New York: Routledge, 1872), pp. 495-507;
109. the essay is dated 8 June 1866. Quetetet did not learn about Herschel's review of his work until 1965. He then asked permission to translate it into French with an introduction. See Adolphe Quetelet to Herschel, 14 Aug. 1865, and Herschel to Quetelet, 14 Aug. 1865, 22 Aug. 1865, abstracted in Herschel, Calendar of the Correspondence of Sir John Herschel, ed. Crowe (cit. n. 20), item nos. 12952, 12953, 12955.
110. Robert Boyle, "Some Considerations about the Reconcileableness of Reason and Religion" (1675), in Works of the Honorable Robert Boyle, 6 vols., Vol. 4 (London, 1772), p. 182.
111. quoted in Lorraine Daston, Classical Probability in the Enlightenment (Princeton, N.J.: Princeton Univ. Press, 1988), p. 63;
112. and "Probabilité," in Encyclopédie, ou Dictionnaire raisonné des sciences, des arts et des métiers, ed. Jean d'Alembert and Denis Diderot, 35 vols. (Paris: Briasson, David l'aîné, Le Breton, Durand, 1751-1780), Vol. 13, p. 393b.
113. On the changing meaning of "moral certainty" see Barbara J. Shapiro, "Beyond Reasonable Doubt" and "Probable Cause": Historical Perspectives on the Anglo-American Laws of Evidence (Berkeley/Los Angeles: Univ. California Press, 1991), pp. 7-12;
114. Shapiro, Probability and Certainty in Seventeenth-Century England: A Study of the Relationships between Natural Science, Religion, History, Law, and Literature (Princeton, N.J.: Princeton Univ. Press, 1983), pp. 36-37;
115. and Steven Shapin, A Social History of Truth: Civility and Science in Seventeenth-Century England (Chicago: Univ. Chicago Press, 1994), pp. 208-211.
116. Herschel, "Quetelet on Probabilities" (cit. n. 1), pp. 368, 368-369;
117. and Carl Friedrich Gauss to Wilhelm Olbers, 3 May 1827, in Wilhelm Olbers, sein Leben und seine Werke, ed. C. Schilling, 2 vols. (Berlin: Springer, 1894-1909), Vol. 2, pp. 479-482, on p. 480 (I thank Lorraine Daston for calling this letter to my attention).
118. Herschel, "Quetelet on Probabilities," p. 391.
119. On Buffon's argument see Daston, Classical Probability in the Enlightenment (cit. n. 51), pp. 91-95.
120. In his review of Herschel's Preliminary Discourse Whewell described the first chapter as "one of the finest essays on the moral conduct of the intellect which has ever been produced": [William Whewell], "[Review of] A Preliminary Discourse on the Study of Natural Philosophy," Quart. Rev., 1831, 45:374-407, on p. 406.
121. See also Yeo, Defining Science (cit. n. 25), p. 120.
122. William Whewell, Astronomy and General Physics Considered with Reference to Natural Theology (London: William Pickering, 1833), p. 329 (in 1838 Whewell became Professor of Moral Philosophy at Trinity College);
123. Herschel, "Whewell on the Inductive Sciences" (cit. n. 26), p. 189;
124. and Herschel, "Address to the British Association for the Advancement of Science, 1845" (cit. n. 32), pp. 667-668,
125. quoted in Yeo, Defining Science, p. 179.
126. Whewell to J. C. Hare, 25 Dec. 1833, in I. Todhunter, William Whewell, DD., Master of Trinity College Cambridge: An Account of the Writings with Selections from His Literary and Scientific Correspondence, 2 vols., Vol. 2 (London: Macmillan, 1876), pp. 174-176, on p. 175;
127. and Thomas Rawson Birks, Oration on the Analogy of Mathematical and Moral Certainty (Cambridge, 1834), pp. 2, 17, 30-31. The "living author" was probably Samuel Taylor Coleridge, although I have been unable to find the exact citation.
128. This is Ian Hacking's phrase: Hacking, The Taming of Chance (Cambridge: Cambridge Univ. Press, 1990), p. 2.