Isaac Newton (31 page)

12
. Newton seems to have drafted this dispensation himself. No one knows how he gained royal approval; perhaps Barrow interceded for him.

13
. Yahuda MS 14, quoted in Westfall,
Never at Rest
, p. 315.

14
. Ibid., p. 317 n.

15
. Westfall, “Newton’s Theological Manuscripts,” in Bechler,
Contemporary Newtonian Research
, p. 132.

16
. “A Short Schem of the True Religion,” Keynes MS 7, in Cohen and Westfall,
Newton: Texts
, p. 345.

11: FIRST PRINCIPLES

1
. Add MS 404.

2
. But this was not “Halley’s comet.” That came next, in 1682. It was not till 1696—having ingested the revelations of Newton’s
Principia
and having obtained data from a now-hostile Flamsteed—that Halley calculated its path as an ellipse rather than a parabola and predicted its return every seventy-six years.

3
. Andrew P. Williams, “Shifting Signs: Increase Mather and the Comets of 1680 and 1682,”
Early Modern Literary Studies
1: 3 (December 1995).

4
. Flamsteed to Crompton for Newton, December 15, 1680,
Corres
II: 242.

5
. Schaffer, “Newton’s Comets and the Transformation of Astrology,” p. 224. Indeed, Hooke had been suggesting that comets might orbit the sun with periods of many decades and that the paths of comets might be bent into a curve by the attractive power of the sun. Pepys,
Diaries
, March 1, 1665; Hooke,
Cometa
, 1678.

6
. Flamsteed to Crompton, January 3, 1681,
Corres
II: 245.

7
. Flamsteed to Crompton, February 12, 1681,
Corres
II: 249.

8
. Flamsteed to Halley, February 17, 1681,
Corres
II: 250.

9
. Newton to Crompton for Flamsteed, February 28, 1681,
Corres
II: 251. It is now clear that the data available to Newton were riddled with errors and inconsistencies, some even caused by confusion over calendar differences.

10
. “The only way to releive this difficulty in my judgmt is to suppose the Comet to have gone not between the
and the Earth but to have fetched a compass about the
.” Ibid.

11
. Hooke to Newton, November 24, 1679,
Corres
II: 235.

12
. Newton to Hooke, November 28, 1679,
Corres
II: 236.

13
.
An Attempt to Prove the Motion of the Earth by Observations
(London: John Martyn, 1674). Hooke implied, but did not state mathematically, that gravity was inversely proportional to distance: “these attractive powers are so much more powerful in operating, by how much nearer the body wrought upon is to their own Centers.”

14
. Newton to Hooke, November 28, 1679,
Corres
II: 236. Hooke took this for a lie: “He here pretends he knew not H’s hypothesis,” he wrote on the letter. And he was right. Newton admitted it to Halley in 1686. Cf. Koyré, “An Unpublished Letter of Robert Hooke to Isaac Newton,” in
Newtonian Studies
, p. 238 n., and Westfall,
Never at Rest
, p. 383 n.

15
. Newton to Hooke, November 28, 1679,
Corres
II: 236.

16
. The discussion that followed shows, as Koyré says, “the level of understanding—or lack of understanding—of even the best minds of the time.” Christopher Wren suggested shooting a bullet almost straight up, but “round every way,” to see if the bullets all fall in a perfect circle. Flamsteed said it was well known that a ball shot directly upward would not fall back into “the mouth of the piece”; he suggested an angle of 87 degrees. Koyré,
Newtonian Studies
, p. 246.

17
. Hooke to Newton, December 9, 1679. Newton had made a double error, in fact, because he also noted that such an object dropped in the Northern Hemisphere would tend southward as well as eastward. But there are complexities. Hooke was assuming a vacuum; as Newton later pointed out, the path through a resisting medium such as air would in fact be a spiral reaching the earth’s center. Also, neither man was ready (at first) to work out what it meant, gravitationally, to consider the earth’s mass as spread through a sphere extending outside the path of the falling object, rather than concentrated at a central point. Koyré,
Newtonian Studies
, p. 248, and
Corres
II: 237.

18
. He later told Halley, “I refused his correspondence, told him I had laid Philosophy aside,… expected to hear no further from him, could scarce perswade my self to answer his second letter; did not answer his third.” Newton to Halley, June 20, 1686,
Corres
II: 288.

19
. Hooke placed the center of the earth incorrectly at the ellipse’s center, rather than at a focus. Hooke to Newton, December 9, 1679,
Corres
II: 237; Newton to Hooke, December 13, 1679,
Corres
II: 238.
   A thorough and persuasive analysis of these diagrams and what they reveal about Newton’s understanding of the possibilities—backward to his first mathematics on curvature and forward to the
Principia
—is J. Bruce Brackenridge and Michael Nauenberg, “Curvature in Newton’s Dynamics,” in Cohen and Smith,
Cambridge Companion to Newton
.

20
. Hooke to Newton, January 6, 1680,
Corres
II: 239.

21
. Hooke to Newton, January 17, 1680,
Corres
II: 240.

22
. “Mr. Hook then sd that he had it, but that he would conceale it for some time that others triing and failing, might know how to value it, when he should make it publick.” Halley to Newton, June 29, 1686,
Corres
II: 289.

23
. Add MS 3965,
De Motu Corporum
, in Hall and Hall,
Unpublished Scientific Papers
, p. 241.

24
.
De Motu Corporum in Gyrum
, in Herivel,
Background to Newton’s Principia
, pp. 257–89.

25
. Flamsteed to Newton, December 27, 1684,
Corres
II: 273. Flamsteed did eventually see it.

26
. Flamsteed to Newton, December 27, 1684, and January 12, 1685,
Corres
II: 273 and 276.

27
. Humphrey Newton’s recollections, quoted in Westfall,
Never at Rest
, p. 406.

28
.
Principia
382.

29
. “… the manner of expression will be out of the ordinary and purely mathematical.… Accordingly those who there interpret these words as referring to the quantities being measured do violence to the Scriptures. And they no less corrupt mathematics and philosophy.…”
Principia
414.

30
.
Principia
408.

12: EVERY BODY PERSEVERES

1
. Birch,
History of the Royal Society
, 4: 480

2
. Humphrey Newton (no relation).

3
. Birch,
History of the Royal Society
, 4: 480

4
. Halley to Newton, May 22, 1686,
Corres
II: 285.

5
. Newton to Halley, May 27, June 20, July 14, and July 27, 1686,
Corres
II: 286, 288, 290, 291.

6
. Westfall,
Never at Rest
, p. 449. Having obliterated Hooke, he gave early and prominent mention to “Sir Christopher Wren, Dr. John Wallis, and Mr. Christiaan Huygens, easily the foremost geometers of the previous generation.”
Principia
424.

7
. Newton to Halley, June 20, 1686,
Corres
II: 288.

8
. Francis Willoughby and John Ray,
Historia Piscium
(London: John Martyn, printer to the Royal Society, 1678).

9
. Halley to Newton, February 24, 1687,
Corres
II: 302.

10
. Halley to Newton, July 5, 1687,
Corres
II: 309.

11
.
Phil. Trans
. 16: 291.

12
.
Principia
416–17.

13
. Cf. J. R. Milton, “Laws of Nature,” in Garber and Ayers,
Cambridge History of Seventeenth-Century Philosophy
, p. 680. The practice of naming “laws” after their scientific discoverers did not exist; it was born here. Kepler’s laws antedate Newton’s, but
Kepler’s laws
is an eighteenth-century backformation.

14
.
Natura valde simplex est et sibi consona
. “Conclusio” (Add MS 4005), in Hall and Hall,
Unpublished Scientific Papers
, p. 333.

15
. Modern students of physics, with the calculus in their arsenal, often find it simple to derive a result of Newton’s by calculus yet difficult to understand the same result in the geometrical terms Newton employed in the
Principia
. Newton foresaw this himself. Thirty years later, he gave an anonymous account, writing of himself in the third person:

By the help of the new
Analysis
Mr. Newton found out most of the Propositions in his
Principia Philosophiæ
; but because the Ancients for making things certain admitted nothing into geometry before it was demonstrated synthetically, that the Systeme of the Heavens might be founded upon good Geometry. And this makes it now difficult for such unskillful men to see the Analysis by which those Propositions were found out.
Phil. Trans
. 29 (1715): 206.

Newton made this and similar self-serving claims about his use of the calculus in the course of his dispute with Leibniz about which of them had invented it. Scholars have debated it endlessly. They have found nothing like a discarded draft of the
Principia
in terms of the new analysis.

16
.
Principia
442.

17
.
Principia
590.

18
. Recalled after Newton’s death by Conduitt, at second or third hand. Keynes MS 130.6.

19
.
Principia
793 and Keynes MS 133.

20
.
Principia
790.

21
.
Principia
803.

22
. Here and in several other calculations, he was not above manipulating the numbers to produce the appearance of exactitude. No one called his bluff. Galileo, in a comparable position, had elected to stay away from precise numerical calculations, saying that such vagaries as air resistance do not “submit to fixed laws and exact description.… It is necessary to cut loose from such difficulties.” Newton, by contrast, set himself, and science, the obligation to exclude nothing and calculate everything. As Westfall says, “So completely has modern physical science modeled itself on the
Principia
that we can scarcely realize how unprecedented such calculations were.” It was impossible, given the available data, and sometimes he cheated. Westfall, “Newton and the Fudge Factor,”
Science
179 (February 23, 1973): 751. Also Nicholas Kollerstrom, “Newton’s Lunar Mass Error,”
Journal of the British Astronomical Association
95 (1995): 151. For another example of what Whiteside calls “the delicate art of numerical cookery,” see
Math
VI: 508–36.