Newton and the Counterfeiter (32 page)

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 "any demonstrations of them": Abraham de Moivre, "Memorandum relating to Sr Isaac Newton given me by Mr Demoivre," Cambridge Add. Ms. 4007, pp. 706–r, cited in D. T. Whiteside, "Sources and Strengths of Newton's Early Mathematic Thought," in Robert Palter, ed.,
The
Annus Mirabilis
of Sir Isaac Newton, 1666–1696,
p. 72.
the meals he forgot to eat: Nicholas Wickens reported on Newton's indifference to sleep and food in a letter to Robert Smith, 16 January 1728, in which he described his father's memories of his chamber mate. Keynes Ms. 137, sheet 2. John Conduitt told the story of the cat's avoirdupois in his memoirs of Newton, Keynes Ms. 130.6, cited in Richard Westfall,
Never at Rest,
pp. 103–4.

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 "except God": Isaac Newton,
Quœstiones quœdam Philosophicœ,
Cambridge Add. Ms. 3996, f. 1/88. The quoted material comes from page 338 in the excellent transcript of the
Quœstiones
in J. E. McGuire and Martin Tamny,
Certain Philosophical Questions,
pp. 330–489.

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 the point of his needle: Isaac Newton, Cambridge Add. Ms. 3975, reproduced in Richard Westfall,
Never at Rest,
p. 95.

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 "Great fears of the Sicknesse": Samuel Pepys,
The Shorter Pepys,
p. 486.
"which took away the apprehension": Ibid., p. 494.

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 "such a calamity as this": Daniel Defoe,
A Journal of the Plague Year,
pp. 62–63.
"on occasion of the Pestilence": Cited in Richard Westfall,
Never at Rest,
p. 142.

2. "T
HE
P
RIME OF
M
Y
A
GE
"

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 "a perfect cure of the plague": Samuel Pepys,
The Shorter Pepys,
p. 557.
"Mathematicks & Philosophy": Cambridge Add. Ms. 3968.41, f. 85, cited in Richard Westfall,
Never at Rest,
p. 143.
infinitesimally small forms: D. T. Whiteside, ed.,
The Mathematical Papers of Isaac Newton,
vol. 1, p. 280.
Newton returned to Trinity College: Richard Westfall,
Never at Rest,
p. 142.

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 "rays of gravity": Isaac Newton,
Quœstiones quœdam Philosophicœ,
Cambridge Add. Ms. 3996, f. 19.
heavy with fruit: John Conduitt reported a conversation he had with Newton in the last year of his life, 1726. Abraham de Moivre recorded another mention of the apple tree in a memorandum composed in 1727.

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 "thro' the universe": William Stukeley,
Memoirs of Sir Isaac Newton's Life,
pp. 19–21.
A sliver of the old tree: D. McKie and G. R. de Beer, "Newton's Apple: An Addendum,"
Notes and Records of the Royal Society of London
9, no. 2 (May 1952), pp. 334–35.
Newton's apple itself is no fairy tale: D. McKie and G. R. de Beer, "Newton's Apple,"
Notes and Records of the Royal Society of London
9, no. 1 (October 1951), pp. 53–54. Cuttings from Newton's tree have now been propagated in several locations and are for sale by Deacon's Nursery on the Isle of Wight. One cutting, given to my home institution, the Massachusetts Institute of Technology, produced its first fruit in September 2006, in a small garden next to Building 11. At Woolsthorpe, an old Flower of Kent—bearing tree still drops fruit in the garden there. This tree shoots up from a bent-over section of trunk, presumably the blown-down remnants of the Newtonian original.

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 did not publish his result until 1673: For a more detailed account of Newton's derivation of the formula for centrifugal force, see D. T. Whiteside, "The Prehistory of the
Principia," Notes and Records of the Royal Society of London
45, no. 1 (January 1991), p. 13. Richard Westfall presents a less technical version in
Never at Rest,
pp. 148–50, which draws on J. W. Herivel's article "Newton's Discovery of the Law of Centrifugal Force,"
Isis
51 (1960), pp. 546–53, and his book
The Background to Newton's
Principia.
the centrifugal push: Isaac Newton,
Correspondence 3,
46–54. See D. T. Whiteside, "The Prehistory of the
Principia, Notes and Records of the Royal Society of London
45, no. 1 (January 1991), pp. 14–15, for a discussion of Newton's analysis of the motion of a pendulum.

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 would come to be called gravity: This is not quite accurate. Objects under the influence of gravity travel around the center of mass of the total system, not just of the more massive body, as Newton in fact understood. At this time Newton did not have a clear understanding of the concept of inertia, nor yet his first law of motion, which holds that objects at rest or in linear motion tend to stay in motion or at rest unless acted upon by an exterior force. Without this fundamental idea, first suggested to Newton by Robert Hooke in a letter in 1679, his conception of gravity remained imprecise. See Richard Westfall,
Never at Rest,
pp. 382–88, for a discussion of both the insight and the conflict between Hooke and Newton that followed. See also S. Chandrasekhar's summary of the sequence of development of Newton's thinking in the first chapter of his
Newton's
Principia
for the Common Reader,
pp. 1–14. (Note, however, that I. Bernard Cohen, one of the great Newton scholars of the twentieth century and the translator of the best available English version of the
Principia,
does not think highly of Chandrasekhar's historical skills, and it is true, as Cohen says, that the "common reader" of Chandrasekhar's title had better know a lot of mathematics to make it through most of the argument. Nonetheless, Chandrasekhar, a Nobel laureate in physics, does offer a good introductory summary of the basic concepts in the first section of his book, and it is worth a look.) Another good account of the development of Newton's thoughts on gravity during this period comes in A. Rupert Hall's highly readable biography
Isaac Newton: Adventurer in Thought,
pp. 58–63.
"sixty measured Miles only": William Whiston,
Memoirs of the Life of Mr. William Whiston by himself,
cited in J. W. Herivel,
The Background to Newton's
Principia, p. 65. Whiston was a Newton protégé and his successor to the Lucasian professorship at Cambridge. The circumference of the earth at the equator is 24,902 miles, or 40,076 kilometers. One degree, or
¹
/
₃₆₀
, of that total is 69.172 miles, or 111.322 kilometers. D. T. Whiteside points out that Whiston may not be a reliable source—even though he was Newton's successor as Lucasian Professor, his notes on Newton's life were composed after his predecessor had died. The earliest surviving calculation in Newton's hand that analyzes the motion of the moon subject to an attractive force decreasing with the square of the distance from the earth comes no earlier than 1669, three years after the plague season. Still, it is clear that Newton's work on the problem began while he was sheltering from the epidemic. See D. T. Whiteside, "The Prehistory of the
Principia,
" pp. 18–20. My thanks to Simon Schaffer for advice on picking through the minefield of memory and determined fact that stretches across the history of the miracle years. All errors that remain are, of course, mine, not his.

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 "subjecting motion to number": The phrase "subjecting motion to number" is borrowed from Alexander Koyré's marvelous essay "The Significance of the Newtonian Synthesis," which has been published a number of times but is most accessible in I. Bernard Cohen and Richard Westfall, eds.,
Newton,
p. 62. I appropriate the line with an apology: Koyré applied it to Galileo, but it is just as true of Newton.
"mutation in its state": J. W. Herivel,
The Background to Newton's
Principia, pp. 157–58.

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 "a Chair to sit down in": Humphrey Newton, Keynes Ms. 135, quoted in Richard Westfall,
Never at Rest,
p. 406. I have corrected a misspelling in the original document of the name Alchimedes and have rendered the "eureka" in English instead of the original's Greek.
the landlocked Newton sought out data: Simon Schaffer has pointed out Newton's use of a global knowledge network in several papers. See Schaffer's "Golden Means: Assay Instruments and the Geography of Precision in the Guinea Trade" and his as yet unpublished "Newton on the Beach," a lecture delivered at Harvard University on April 4, 2006.

3. "I H
AVE
C
ALCULATED
I
T
"

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"read to y
^e
Walls": Humphrey Newton to John Conduitt (Newton's nephew-in-law and successor as Master of the Mint), 17 January 1727/8, Keynes Ms. 135, f. 2, available at the Newton online archive,
http://www.newtonproject.sussex.ac.uk
. Newton did not in fact fully satisfy even the minimum requirements of the post. He did lecture regularly on algebra but failed to place any manuscripts in the university library until 1684, when he handed over a text covering eleven years' worth of lectures. The work was later published as
Arithmetica universalis.

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 "not enduring to see a weed in it": Humphrey Newton to John Conduitt, 17 January 1727/8, Keynes Ms. 135, ff. 1–3.
"failure to reach fulfillment": Richard Westfall,
Never at Rest,
p. 407.

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 "heavenly motions upon philosophical principles": Isaac Newton to Edmond Halley, 27 May 1686,
Correspondence 2,
p. 433.
a book worth forty shillings: In fact, this was a substantial offer, roughly a week's stipend for someone holding an endowed chair at Cambridge. Books were still scarce and valuable enough that the Royal Society would ultimately try to pay Halley for the trouble and expense of his seeing the
Principia
through publication with fifty copies of another Royal Society title,
The History of Fishes.
(The society also tried to do the same to cover Robert Hooke's back wages, but Hooke refused, preferring to wait for the cash he eventually received.)
"as good as his word": Edmond Halley to Isaac Newton, 29 June 1686,
Correspondence 2,
pp. 441–43.
"renew it & send it to him": Newton's account as reported by Abraham de Moivre, a mathematician and Huguenot refugee to London who knew both Halley and Newton. The original is in the Joseph Halle Schaffner Collection of the University of Chicago Library, Ms. 1075–77. The passage is quoted in Alan Cook,
Edmond Halley,
p. 149. There is a slightly fishy smell to Newton's claim to have lost the earlier demonstration, since historians have identified in his papers a document that is either the "lost" original or a version with corrections, which implies that Newton still possessed his earlier calculation when he spoke with Halley. It may be that Newton recognized a flaw in the earlier work, one that he had to correct before showing it to Halley—and certainly before he allowed the dangerous Hooke to see it. Hooke had previously caught a mistake in another demonstration, and Newton had no desire to endure that kind of humiliation again. See Richard Westfall,
Never at Rest,
p. 403.

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 an inverse square attraction: For a marvelous and highly readable account of Newton's proof that inverse square attraction generates Keplerian orbits, see David L. Goodstein and Judith R. Goodstein,
Feynman's Lost Lecture.
In that book, the Goodsteins provide a history of the problem of the shapes of orbits, and then describe how Richard Feynman reconstructed Newton's proof (in its final form, as published in the
Principia).
only closed path: Formally, a truly circular orbit is possible, as a circle is simply the limit of an ellipse when its eccentricity goes to zero. In physically realistic situations, though, this solution is vanishingly unlikely. Thanks to Caltech's Sean Carroll for pointing out this subtlety.

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he did not choose to share: See
Correspondence 2,
documents 272, 274, 276, 278, 280, 281, 284.
"all my results together": Isaac Newton,
Principia,
p. 383.
"any motions whatever": Ibid., p. 382.
"to change its state by forces impressed": Ibid., p. 416.
"A change in motion is proportional": Ibid.

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 "always equal and always opposite": Ibid., p. 417.
seemingly simple point of origin: The first edition of the
Principia
contained 510 pages; 210 in Book One, 165 in Book Two, and 110 in Book Three, with the rest given over to introductory remarks and other apparatus.

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 "the Hour of Prayer": Humphrey Newton to John Conduitt, 17 January 1727/8, Keynes Ms. 135, ff. 2–3.
"less to clarify the celestial motions": Isaac Newton,
Principia,
p. 790.
"to demonstrate the other phenomena": Ibid., p. 382.
"from these same principles": Ibid., p. 793.

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 properties of bodies anywhere: In Newton's words, this "rule for the study of natural philosophy" reads: "Those qualities of bodies that cannot be intended and remitted [i.e., qualities that cannot be increased and diminished] and that belong to all bodies on which experiment can be made should be taken as qualities of all bodies universally." Ibid., p. 795 (interpolation by the translators).

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 good data from bad: Simon Schaffer, "Newton on the Beach," pp. 14–17. This unpublished lecture, delivered at Harvard University on April 4, 2006, presents a valuable analysis of Newton's approach to measurement and the significance of the worldwide system of observation and knowledge to Newton's science.
the farthest extremes of the heavens: Isaac Newton,
Principia,
pp. 901–16.
"The theory that corresponds exactly": Ibid., p. 916.

4. "T
HE
I
NCOMPARABLE
M
R.
N
EWTON
"

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 a man whom Newton admired: John Locke,
Philosophical Transactions of the Royal Society
24, no. 298, pp. 1917–20. I am grateful to Jan Golinski for leading me to Locke's weather diary.
confinement to ye London air: Newton to Locke (draft),
Correspondence 3,
p. 184.