Isaac Newton

A word about dates. In the time with which we are concerned, the English calendar ran at first ten and then eleven days behind the calendar in most of Europe. I use the English dates. Meanwhile, the year in England was considered to start March 25, not January 1. So, for example, when Newton died on March 20, they reckoned it was 1726 in England but 1727 elsewhere. From our anachronistic point of view, it was 1727, so I use the Continental—modern—years.

A word about language. Mostly I follow the spelling and style of the original texts. But where Newton (and others) compressed words to “y^e,” “w^ch,” “y^t,” &c., I have modernized the orthography for the sake of readability.

EPIGRAPH Newton’s recollection, the year before he died, of having made the first reflecting telescope; recorded by his niece’s husband, John Conduitt, memorandum, August 31, 1726, Keynes MS 130.10.

1. “What a lesson to the vanity and presumption of philosophers!” exclaimed his first biographer, Brewster, in 1831 (The Life of Sir Isaac Newton, p. 303). Newton, who read incessantly and remained unsettled, was echoing Milton (Paradise Regained, 320–21):

Who reads

Incessantly, and to his reading brings not

A spirit and judgment equal or superior,

(And what he brings what needs he elsewhere seek?)

Uncertain and unsettled still remains,

Deep-versed in books and shallow in himself,

Crude or intoxicate, collecting toys

And trifles for choice matters, worth a sponge,

As children gathering pebbles on the shore.

3. Having compared them as lovers, Voltaire added judiciously, “One can admire Newton for that, but must not blame Descartes.” Letters on England, 14, pp. 68–70.

4. Nor did he persuade us quickly. A few years before his death, a scholarly author could rail against Newton’s conception of gravity (“this Cause, which looks as monstrous as any of the Fictions of Antiquity”) without condescending to use the word: “That it is a Virtue or Power which Bodies have to attract or draw one another; that every Particle of Matter has this Power or Virtue; that it reaches to all Places at all Distances, and penetrates to the Center of the Sun and Planets; that it acts not upon the Surfaces of Bodies as other Natural Agents, but upon their whole Substance or solid Content, &c. and if so, what a strange Thing must it be.” Gordon, Remarks, p. 6.

5. Hermann Bondi, “Newton and the Twentieth Century—A Personal View,” in Fauvel et al., Let Newton Be!, p. 241.

7. As Einstein himself knew well. Hermann Bondi commented: “When I talk on special relativity, I always say that Einstein’s contribution has a name for being difficult, but this is quite wrong. Einstein’s contribution is very easy to understand, but unfortunately it rests on the theories of Galileo and Newton which are very difficult to understand!” “Newton and the Twentieth Century—A Personal View,” in Fauvel et al., Let Newton Be!, p. 245.

1: WHAT IMPLOYMENT IS HE FIT FOR?

1. Barnabas Smith was sixty-three and well off; Hannah Ayscough probably about thirty; their marriage was negotiated by one of the rector’s parishioners, for a fee, and by her brother. It was agreed that Isaac would remain at Woolsthorpe and that Smith would give him a parcel of land. She brought to the marriage a parcel with an income of £50.

2. One skirmish broke out near Grantham on May 13, 1643; fighting continued sporadically nearby through the summer and occasionally during the rest of the decade.

4. Merchants were expected to “have knowledge and cunning in reading and writing” as well as “the knowledge and feate of Arithmetike,” if not with pen then with counters on a board. Hugh Oldcastle, A Briefe Introduction and Maner how to keepe Bookes of Accompts (1588), quoted in Thomas, “Numeracy in Modern England,” p. 106.

5. When he was twenty, a student at Trinity College, he suffered a sort of crisis of conscience around Whitsunday and wrote down—in a private shorthand—a catalogue of his sins. Among the early sins he included “Threatning my father and mother Smith to burne them and the house over them” and “Wishing death and hoping it to some.” He also recalled “peevishness” with his mother and half-sister, striking his sister and others, “having uncleane thoughts words and actions and dreamese,” and many episodes of lying and violating the Sabbath (“Thy day”). Westfall, “Short-Writing and the State of Newton’s Conscience,” p. 10.

6. Stukeley, Memoirs, p. 43: “He showd another method of indulging his curiosity to find out the sun’s motion, by making dyals of divers forms and constructions every where about the house, in his own chamber, in the entrys and rooms where ever the sun came.”

8. Stukeley, Memoirs, p. 43 “and made a sort of almanac of these lines, knowing the day of the month by them, and the suns entry into signs, the equinoxes and solstices. So that Isaacs dyals, when the sun shined, were the common guide of the family and neighborhood.”.

“It is indeed a matter of great difficulty to discover and effectually to distinguish the true motions of particular bodies from the apparent, because the parts of that immovable space in which those motions are performed do by no means come under the observation of our senses. Yet the thing is not altogether desperate; for we have some arguments to guide us, partly from the apparent motions, which are the differences of the true motions; partly from the forces, which are the causes and effects of the true motions. For instance, if two globes, kept at a given distance one from the other by means of a cord that connects them, were revolved about their common center of gravity, we might, from the tension of the cord, discover the endeavor of the globes to recede from the axis of their motion, and from thence we might compute the quantity of their circular motions.…” Principia (Motte), p. 12.

12. Stukeley, Memoirs, p. 43. Other, presumably Newtonian, crude diagramming has been uncovered. Whiteside (“Isaac Newton: Birth of a Mathematician,” p. 56) assessed them coolly: “It would need the blindness of maternal love to read into these sets of intersecting circles and scrawled line-figures either burgeoning artistic prowess or mathematical precocity.”

13. It was long thought that Newton had no mathematical training as a schoolboy, but Stokes’s own notebook, “Notes for the Mathematicks,” exists in the Grantham Museum (D/N 2267). Whiteside, “Newton the Mathematician,” in Bechler, Contemporary Newtonian Research, p. 111. For acres cf. Petty, Political Arithmetick, and John Worlidge, Systema Agriculturæ (London: Dorling, 1687).

14. Quoted in Manuel, Portrait, pp. 57–58. The “Latin Exercise Book,” originally among the papers of the Portsmouth Collection, is in private hands. Manuel adds: “There is an astonishing absence of positive feeling. The word love never appears, and expressions of gladness and desire are rare. A liking for roast meat is the only strong sensuous passion.”

16. More fully: “Though there were many Giants of old in Physick and Philosophy, yet I say with Didacus Stella: A dwarf standing on the shoulders of a Giant may see farther than the Giant himself; I may likely add, alter, and see farther than my predecessors.” This is neither the beginning nor the end of the story of this aphorism. For that, one must read Merton, On the Shoulders of Giants.

19. This notebook was mentioned soon after his death by his niece’s husband, John Conduitt; then it disappeared for several centuries; then it reappeared in the 1920s in the possession of the Pierpont Morgan Library, where it remains (MA 318). Cf. David Eugene Smith, “Two Unpublished Documents of Sir Isaac Newton,” in Greenstreet, Isaac Newton, pp. 16–34; Andrade, “Newton’s Early Notebook”; and the original Bate, Mysteryes.

22. Dictionaries and encyclopedias (“circles” of knowledge) barely existed, but he might have seen John Withals, A Shorte Dictionarie for Yonge Begynners (1556), which arranges words under subject headings; Robert Cawdry, Table Alphabeticall Contayning and Teaching the True Writing and Understanding of Hard Usuall English Words (1604); Francis Gregory, Nomenclatura Brevis Anglo-Latinum.

2: SOME PHILOSOPHICAL QUESTIONS

2. A few years later, as a new undergraduate at Cambridge, he drew diagrams from memory that illustrate classic fluid mechanics—or rather, what would have been fluid mechanics, had this science yet been invented. He guessed to associate air and water resistance: “… for you may observe in water that a thing moved in it doth carry the same water behind it … or at least the water is moved from behind it with but a small force as you may observe by the motes in the water … the like must hapen in aire.…” Questiones, “Of Violent Motion,” Add MS 3996, p. 21.

3. From a list of sins he set down three years later: “Refusing to go to the close at my mothers command”; “Punching my sister”; “Peevishness with my mother”; “With my sister.” Westfall, “Short-Writing and the State of Newton’s Conscience,” pp. 13f.

5. Trinity College Note Book, MS R4.48. His tutor was Benjamin Pulleyn. He had chamber fellows but formed no friendships.

6. Notebook in the Fitzwilliam Museum, Cambridge, as transcribed by Westfall, “Short-writing and the State of Newton’s Conscience.” Westfall comments: “We are forced to conclude either that Newton’s young manhood had been remarkably pure or that his power of self-examination was remarkably under-developed. Probably we should reach both conclusions.”

7. Edward Ward, A Step to Stir-Bitch-Fair (London: J. How, 1700); Daniel Defoe, Tour through the Whole Island of Great Britain (1724). Stourbridge Fair was the model for Vanity Fair in John Bunyan’s Pilgrim’s Progress.

9. And “becoming hot or sweet or thick or dry or white.” Aristotle, Physics, trans. R. P. Hardie and R. K. Gaye, VII: 2.

12. Cf. ibid., III: 1: “It is the fulfillment of what is potential when it is already fully real and operates not as itself but as movable, that is motion. What I mean by ‘as’ is this: Bronze is potentially a statue.”

13. Exception: Sidereus Nuncius, published in Venice in 1610. Newton acquired a version of this when he was in his forties (Harrison, The Library of Isaac Newton, p. 147). It was first translated into English in 1880.

14. Some biographers have suggested that Newton invented this phrase, but Aristotle expresses the sentiment in Nicomachean Ethics I: 6, and the Latin motto is attributed to him in Diogenes Laërtius, De vitis dogmatibus et apophtegmatibus clarorum philosophorum, a copy of which Newton owned. For more exhaustive detective work on the slogan see Guerlac, “Amicus Plato and Other Friends,” in Newton on the Continent.
As he wrote, Newton was reading closely—and sometimes disputing—Walter Charleton (Physiologia Epicuro-Gassendo-Charltoniana), Descartes (a partial collected works, in Latin), the Platonist Henry More (The Immortality of the Soul) and the contemporary experimenter Robert Boyle. The definitive analysis of the Questiones, including a careful transcription, is McGuire and Tamny, Certain Philosophical Questions.
The notebook is in the Cambridge University Libraries as Add MS 3996. My citations use Newton’s page numbers.

21. Coastal-dwelling people in every part of the world had noticed coincidences in timing between the flow of tides and the changing of the moon, as well as the sun. Near shores and harbors of the North Atlantic, in particular, monks had been saving data—though not disseminating it—for hundreds of years.

3: TO RESOLVE PROBLEMS BY MOTION

1. Conduitt, “Memorandum relating to Sr Isaac Newton given me by Mr Demoivre in Novr 1727”:

In 63 being at Stourbridge fair bought a book of Astrology … Read in it till he came to a figure of the heavens which he could not understand for want of being acquainted with Trigonometry. Bought a book of Trigonometry, but was not able to understand the Demonstrations. Got Euclid to fit himself for understanding the ground of Trigonometry. Read only the titles of the propositions, which he found so easy to understand that he wondered how any body would amuse themselves to write any demonstrations of them. Began to change his mind when he read that Parallelograms upon the same base & between the same Parallels are equal, & that other proposition that in a right angled Triangle the square of the Hypothenuse is equal to the squares of the other two sides.

2. Thus Whiteside: “We are, too, perhaps a little disappointed that Newton read so little of standard contemporary mathematical works, or if he did has left no hint—nowhere in his early autograph papers do we find the names of Napier, Briggs, Desargue, Fermat, Pascal, Kepler, Torricelli, or even Archimedes and Barrow.” “Sources and Strengths of Newton’s Early Mathematical Thought,” in Palter, Annus Mirabilis, p. 75. Apart from Newton’s notes, his second- and third-hand recollections of his reading, including the “book of Astrology,” survive in an account by Abraham DeMoivre (Add MS 4007); also Corres VII: 394.

3. Some survived infection, but not many. In Cambridge the final “Plague Bill” reported a total of 758 deaths from June 5 to January 1, all but nine from the plague. About half that number were infected and recovered. Leedham-Green, Concise History, p. 74.

4. This is the only surviving letter either to or from Newton’s mother (or, for that matter, any close relative). The edges are torn and some words are missing. Corres I: 2.

6. The “year”—traditionally seen by Newtonians as the annus mirabilis—covered eighteen or twenty or twenty-five months. Sophisticated Newtonians sometimes prefer to speak of the “myth” of the annus mirabilis. For example, Derek Gjertsen debunks the myth sternly: “The description is clearly misleading, for … no special priority can be given to either 1665 or 1666.… It remains true, none the less, and without too much exaggeration, that in a remarkably short period the twenty-four-year-old student created modern mathematics, mechanics, and optics. There is nothing remotely like it in the history of thought.” Gjertsen, Newton Handbook, p. 24. Cf. Whiteside (“Newton the Mathematician,” in Bechler, Contemporary Newtonian Research, p. 115): “Never did seventeenth-century man build up so great a store of mathematical expertise, much of his own discovery, in so short a time.”
Anyway, Newton’s stay in Woolsthorpe extended over about twenty months, broken by a temporary return to Cambridge in the spring of 1666.

7. Alfred North Whitehead noted that Europe knew less mathematics in 1500 than Greece knew in the time of Archimedes. Davis and Hersh, Mathematical Experience, p. 18.

8. “Thrice happy he, who, not mistook, / Hath read in nature’s mystic book!” Andrew Marvell, “Upon Appleton House, to My Lord Fairfax.”

9. Galileo, Il Saggiatore (1623), in The Controversy on the Comets of 1618, pp.183–84.

11. Whiteside, “Newton the Mathematician,” in Bechler, Contemporary Newtonian Research, pp. 112–13. Newton’s annotated student copy of the Elements, Trinity College Library, NQ.16.201.

12. John Conduitt’s romanticized account (Keynes MS 130.4, in Math I: 15–19):

He then young as he was took in hand Des-Cartes’s Geometry (that book which Descartes in his Epistles with a sort of defiance says is so difficult to understand). He began with the most crabbed studies & books, like a high spirited horse who must be first broke in crabbed grounds & the roughest & steepest ways, or could otherwise be kept within no bounds. When he had read two or three pages & could understand no farther he being too reserved and modest to trouble any person to instruct him begain again & got over three or four more till he came to another difficult place, & then began again & advanced farther & continued so doing till he not only made himself master of the whole without having the least light or instruction from any body, but discovered the errors of Descartes.…

He read it in Schooten’s Latin translation in the summer of 1664. Newton’s own reminiscences of his mathematical development tended to minimize the role of Descartes, but Whiteside’s scholarship is conclusive: that “the thick wad of Newton’s research papers surviving from the later months of 1664 stand firm witness that it was indeed from the hundred or so pages of the Géométrie that his mathematical spirit took fire.… Above all, I would assert, the Géométrie gave him his first true vision of the universalizing power of the algebraic free variable, of its capacity to generalize the particular and lay bare its inner structure.” “Newton the Mathematician,” in Bechler, Contemporary Newtonian Research, p. 114.

But he also filled it with critical marginalia; e.g., “Error, Error, non est Geom” and “Imperf.” Trinity College Library, NQ.16.203.

13. “It seems to be nothing other than that art which they call by the barbarous name of ‘algebra,’ if only it could be disentangled from the multiple numbers and inexplicable figures that overwhelm it …” Descartes, Regulæ ad directionem ingenii, Regula IV: 5.

14. This new-found truth had to be stated explicitly. Mahoney (“The Beginnings of Algebraic Thought”) quotes Descartes: “Those things that do not require the present attention of the mind, but which are necessary to the conclusion, it is better to designate by the briefest symbols than by whole figures: in this way the memory cannot fail, nor will thought in the meantime be distracted by these things which are to be retained.”

15. Keynes MS 130(7), quoted by Christianson, In the Presence of the Creator, p. 66.

16. Biographia Britannica (London, 1760), V: 3241; quoted by Westfall, Never at Rest, p. 174.

17. The recognition of infinite series had begun with algebraic attempts to express pi; Newton’s immediate predecessors, James Gregory and especially John Wallis, were the first to develop their possibilities. In the simplest sense, infinite series are implied immediately by decimal notation; in one of his earliest jotted fragments Newton wrote: “if the fraction 10/3 bee reduced to decimall it will be 3,33333333 &c infinitely. & what doth every figure signifie but a pte of the fraction 10/3 which therefore is divisible into infinite pts.” Questiones, p. 65.

18. Math I: 134–41; Westfall, Never at Rest, pp. 119–21. This was, he saw, another problem in disguise, the calculation of a logarithm. Years later he recalled: “I am ashamed to tell to how many places I carried these computations, having no other business at that time: for then I took really too much delight in these inventions.” Newton to Oldenburg, October 24, 1676, Corres II: 188.

20. Even seventy years later, one of the first post-Newtonian calculus texts, John Colson’s 1737 Method of Fluxions and Infinite Series, broached the dangerous and unfamiliar topic this way: “… that quantity is infinitely divisible, or that it may (mentally at least) so far continually diminish, as at last, before it is totally extinguished, to arrive at quantities which may be called vanishing quantities, or which are infinitely little, and less than any assignable quantity.…” In Cohen and Westfall, Newton: Texts, p. 400.

29. Cf. Math I: 377; Michael Mahoney, “The Mathematical Realm of Nature,” in Garber and Ayers, Cambridge History of Seventeenth-Century Philosophy, p. 725.

31. “To find the velocitys of bodys by the lines they describe.” Math I: 382.

33. Much later he recalled: “When I am investigating a truth or the solution to a Probleme I use all sorts of approximations and neglect to write down the letter o, but when I am demonstrating a Proposition I always write down the letter o & proceed exactly by the rules of Geometry.” Add MS 3968.41.

34. Math I: 377ff., I: 392ff, and I: 400ff. The tract of October 1666 (Add MS 3958) was published for the first time 296 years later in Hall and Hall, Unpublished Scientific Papers, pp. 15–65.

36. As Koyré puts it, “To have achieved this transformation is the undying merit of Newton.… Mathematical entities have to be, in some sense, brought nearer to physics, subjected to motion, and viewed not in their ‘being’ but in their ‘becoming’ or in their ‘flux.’ ” Newtonian Studies, p. 8.

4: TWO GREAT ORBS

1. The last authoritative twentieth-century account of the Scientific Revolution, Steven Shapin’s Scientific Revolution, began, “There was no such thing as the Scientific Revolution, and this is a book about it.”

3. “The appearance of Newton’s Principia in 1687 changed all this.… [It] made continued support for Aristotle’s geocentric cosmology untenable. After 1687, medieval cosmology became irrelevant, because it no longer represented even a minimally plausible alternative to Newtonian cosmology. Unlamented, it simply faded away.” Grant, Planets, Stars, and Orbs, p. 10.

4. Yet I. Bernard Cohen sees the Copernican revolution as “a fanciful invention of eighteenth-century historians.” The revolution, Cohen asserts, “was not at all Copernican, but was at best Galilean and Keplerian.” Revolution in Science, p. x. Meanwhile, Cohen and other scholars suggest that Newton’s reading, wide-sweeping though it became, may have never included Galileo’s Discorsi or anything of Kepler. Nor, at his death, did his considerable library contain any work by Ptolemy, Copernicus, or Tycho. Cf. Whiteside in Math, VI: 3 n. and 6 n.

5. Now we say these were the first two of Kepler’s three “laws.” We conventionally date these to 1609, when he published his great work, Astronomia Nova. He put forth a notion of gravity, too: “Gravity is the mutual tendency of cognate bodies to join each other (of which kind the magnetic force is).” Nevertheless, by the time of the Principia, at the far end of the century, few astronomers accepted Kepler’s ideas as firm truths; nor did Newton, in the Principia, see Kepler as a significant precursor. “It seems clear,” I. B. Cohen remarked, “that there was no Keplerian revolution in science before 1687.” Revolution in Science, p. 132; Whiteside, “Newton’s Early Thoughts on Planetary Motion,” p. 121; Gjertsen, “Newton’s Success,” in Fauvel et al., Let Newton Be!, p. 25.

7. The only mathematics, except that Galileo declared the moon’s distance to be sixty diameters of the earth—off by a factor of two—and made a brief computation of the height of lunar mountains, declaring (correctly) that they were as high as four miles and (incorrectly) that the earth’s mountains never reached as high as one mile. For a moment, it was easier to see the moon than the earth.

8. Two years later: Discourse concerning a New Planet; tending to prove, that it is probable our Earth is one of the Planets. Wilkins also wrote another book cherished by the young Newton, Mathematical Magick.

12. Wilkins, Mathematical and Philosophical Works, pp. 47, 49, 97, 100, 110–13. For flying to the moon, Wilkins did wonder about the cargo problem: “Nor can we well conceive how a man should be able to carry so much luggage with him, as might serve for his viaticum in so tedious a journey.”

13. Ibid., pp. 4 and 13: “For it is probable that the earth of that other world would fall down to this centre, and so mutually the air and fire here ascend to those regions in the other; which must needs … cause a great disorder.…”

16. He copied bits of Wilkins into his Grantham notebook (cf. Manuel, Portrait, p. 11, and Gjertsen, Newton Handbook, p. 612). Wilkins also expounded systems of “secret writing”—how to hide one’s meaning through obscure or invented or encoded characters (Mercury; or, the Secret Messenger, 1641). He became a doctor of divinity and a prominent Parliamentarian, married Oliver Cromwell’s sister, and soon after was made Master of Trinity College, a preferment he held only briefly before being ousted upon the restoration of Charles II. He moved to London and became a council member of the new Royal Society.

17. Herivel, Background to Newton’s Principia, p. 67; Add MS 3968.41; Westfall, Never at Rest, p. 143.

18. The river flows from four memoirists in particular: his niece, Catherine Barton; Marton Folkes, vice-president of the Royal Society; Barton’s husband, John Conduitt; and Newton’s first would-be biographer, William Stukeley. “The notion of gravitation came into his mind,” Stukeley wrote (Memoirs, p. 20), “… occasion’d by the fall of an apple, as he sat in a contemplative mood.”
   Voltaire related the story first in An Essay on Epick Poetry and then in Letters on England (p. 75): “Having retired to the country near Cambridge in 1666, he was walking in his garden, saw some fruit falling from a tree, and let himself drift into a profound meditation on this weight, the cause of which all the scientists have vainly sought for so long and about which ordinary people never even suspect there is any mystery.”
   And Conduitt: “Whilst he was musing in a garden it came into his thought that the power of gravity (which brought an apple from the tree to the ground) was not limited to a certain distance from the earth but that this power must extend much farther than was usually thought. Why not as high as the moon said he to himself.…” Keynes MS 130.4.
   The apple story took on an independent life and evolved over centuries. Perhaps its most wonderful feature is how often, by the twentieth century, the apple was supposed to have struck Newton on the head. This may not have been necessary.
   Westfall argues, appealingly (Never at Rest, p. 155): “The story vulgarizes universal gravitation by treating it as a bright idea.” Of course! Yet it was a bright idea. We feel this deeply. Surely that’s why the story has so rooted itself in our collective consciousness. The bright idea was a crystallization of a preexisting unconscious knowledge—shared by animals and children—that objects fall to the ground. The bright idea was that this behavior implied a force—to be named and then studied and measured. “A bright idea cannot shape a scientific tradition,” Westfall adds, and this, too, seems self-evident. But it did.

19. Galileo, Two New Sciences, p. 166, quoted in Cohen, Franklin and Newton, p. 103.

20. One detailed set of calculations fills the so-called Vellum Manuscript—the reverse side of a lease. Add MS 3958.45; Herivel, Background to Newton’s Principia, pp. 183–191.

21. Where the “cubit” is the distance from elbow to fingertip. Herivel, Background to Newton’s Principia, p. 184.

24. “The cubes of their distances from the Sun are reciprocally as the squares of the numbers of revolutions in a given time: the endeavours of receding from the Sun will be reciprocally as the squares of the distances from the Sun.” Add MS 3958, in Herivel, Background to Newton’s Principia, p. 197; Westfall, Never at Rest, p.152. In the same spirit: Principia, Book III, Proposition 10, Corollary 3 and Corollary 5 (first edition), where Newton explicitly considers the sun’s heating of the planets as a function of distance.

26. Herivel, Background to Newton’s Principia, p. 141. Descartes had proposed such a principle for bodies both in motion and at rest, though not for circular motion. It still defied people’s intuition about moving objects. “That when a thing lies still, unless somewhat else stir it, it will lie still for ever, is a truth that no man doubts of,” Hobbes wrote in 1651. “But that when a thing is in motion, it will eternally be in motion, unless somewhat else stay it, though the reason be the same (namely, that nothing can change itself), is not so easily assented to.” People get tired and stop moving, so they imagine inanimate objects do, too. “From hence it is that the schools say, heavy bodies fall downwards out of an appetite to rest, and to conserve their nature in that place which is most proper for them.” Leviathan, II.

29. Nor was Latin any better. In trying systematically to define concepts in terms of simpler or more basic concepts, he always reached a wall—a problem of infinite regress. Yet he kept trying. In an undated notebook (Add MS 4003): “The terms quantity, duration and space are too well known to be susceptible of definition by other words.

Def. 1. Place [Locus] is a part of space which something fills evenly.

Def. 2. Body [Corpus] is that which fills place.

Def. 3. Rest [Quies] is remaining in the same place.

Def. 4. Motion [Motus] is change of place.”

In Hall and Hall, Unpublished Scientific Papers, pp. 91 and 122.)

5: BODYS & SENSES

8. Letter of John Wallis, quoted in Charles Richard Weld, History of the Royal Society, I: 30; Ornstein, Role of Scientific Societies, pp. 93 and 95; Phil. Trans. 1 (March 1665). Several such societies, on a regional scale, had been formed in Naples and Florence; the next national scientific society, the Académie des Sciences, was founded in Paris four years later.

9. Wallis letter, in Weld, History of the Royal Society, I: 30; Ornstein, Role of Scientific Societies, p. 95.

10. Horace, Epistles I: 1, 14: “Nullius addictus iurare in verba magistri.…”

12. “An Account of a Dog dissected by Mr. Hook,” in Sprat, History of the Royal Society, p. 232; ’Espinasse, Robert Hooke, p. 52.

13. Pepys, Diary, May 30, 1667. “fine experiments … of colours, loadstones, microscopes, and of liquors … among others, of one that did while she was there turn a piece of roasted mutton into pure blood, which was very rare.… After they had shown her many experiments, and she cried out still she was full of admiration, she departed.…”

14. Hooke tracked his internal weather with equal diligence. A typical journal entry: “Slept a second sleep, sweat and

[ejaculation]. Rose at 11. Eat broth drank port. Belly loosned. Much refresht. 2 stools. DH. With Aubery. Haak chesse. To Garaways. With Tompion and Sir J. Mores. at 7 till 9. Belly loose. Smell well amended. Smokd 4 pipes. Chocolat H. 1. Port. Slept. Sweat.”

17. “This Experiment therefore will prove such a one as our thrice excellent Verulam calls Experimentum Crucis, serving as Guide or Land-mark, by which to direct our course in the search after the true cause of Colours. Affording us this particular negative Information, that for the production of Colours there is not necessary either a great refraction, as in the Prisme; nor Secondly, a determination of Light and shadow, such as is both in the Prisme and Glass-ball.” Ibid., p. 54.

18. A “pellucid body,” as Hooke put it, “where there is properly no such refraction as Des Cartes supposes his Globules to acquire a vorticity by.” Ibid.

20. Ibid., p. 55. He did not care to admit what he did not know. “It is not my business in this place to set down the reasons why this or that body should impede the Rays more, others less: as why Water should transmit the Rays more easily, though more weakly than air.”

6: THE ODDEST IF NOT THE MOST CONSIDERABLE DETECTION

3. Math II: 99–150; W. W. Rouse Ball, “On Newton’s Classification of Cubic Curves,” Proceedings of the London Mathematical Society, 22 (1890–91): 104–43.

4. Barrow catered to Newton’s skittishness by telling Collins: “I pray having perused them so much as you thinke good, remand them to me; according to his desire, when I asked him the liberty to impart them to you. And I pray give me notice of your receiving them with your soonest convenience; that I may be satisfyed of their reception; because I am afraid of them; venturing them by the post.” (July 31, 1669, Corres I: 6.) Newton did eventually permit the publication of De Analysi per Æquationes Infinitas—in 1711, when he was sixty-nine.

9. Lectiones opticæ & geometricæ: in quibus phænomenon opticorum genuinæ rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantu (London, 1674). Scholars have debated Newton’s reticence with Barrow. I. Bernard Cohen found it inconceivable that Newton could have withheld his knowledge from Barrow at this crucial point; he speculated that Barrow just lacked the time or inclination to start his optical work anew (Franklin and Newton, p. 52). But, plausibly, Christianson saw “a prima facie case of deceit on Newton’s part, a hypocritical laughing up his sleeve at the work of a man who was about to advance his career” (In the Presence of the Creator, p. 125).

11. Barrow was appointed Royal Chaplain and then, three years later, Master of Trinity College.

13. “So few went to hear Him, & fewer that understood him, that oftimes he did in a manner, for want of Hearers, read to the walls.… usually staid about half an hour, when he had no Auditors he commonly return’d in a 4^th part of that time or less.” Humphrey Newton, quoted by Conduitt, Keynes MS 135; in Math VI:xii n. The historical record contains not a single recollection from anyone who heard Newton lecture.

14. Shapiro, Optical Papers I: 47. This first lecture was delivered in January 1670 and a version deposited in the library, belatedly, in 1674.

15. “I left off my aforesaid Glass-works; for I saw, that the perfection of Telescopes was hitherto limited, not so much for want of glasses truly figured according to the prescriptions of Optick Authors, (which all men have hitherto imagined), as because that Light it self is a Heterogenous mixture of differently refrangible rays.” Newton to Oldenburg, February 6, 1672, Corres I: 40.

16. The original idea of a reflecting telescope seems to have been James Gregory’s, though Gregory never succeeded in building one. Corres I: 159.

19. Indeed, in 1664 they appointed a committee for improving the English language. It never produced anything definite. (Lyons, Royal Society, p. 55.)

21. Galileo to Mark Welser, May 4, 1612, trans. Stillman Drake, in Discoveries and Opinions of Galileo, p. 92.

23. Samuel Sorbière, A Voyage to England (1709), quoted in Hall, Henry Oldenburg, p. 52.

24. Transactions was a plausible word for this new creature, the serial publication, though the word did not stick. The terms journal and periodical did not yet exist in this context. Words like gazette, pamphlet, and tract had unpleasant connotations, as Adrian Johns notes (“Miscellaneous Methods,” p. 162).
The Philosophical Transactions stands as the first scientific journal, almost. Derek Gjertsen notes that the Academia del Cimento began printing its proceedings in 1657 and continued for about ten years, and that the Journal des Sçavans began appearing in Paris two months before the Philosophical Transactions but encompassed history and law as well as natural philosophy. Newton Handbook, p. 431. About three hundred copies of the first issue were sold. The journal never came close to bringing Oldenburg the profit he hoped for.

31. The telescope, or “perspectives,” did not make a deep impression on all assembled. John Evelyn, later famous for his diaries, recorded the event this way: “To the R. Society; where were produced new invented Perspectives, a letter from Grene-land, of recovering men that had ben drown’d, we had also presented from Iseland some of the Lapis Obsidialis.” Diary of John Evelyn, III: 601.

7: RELUCTANCY AND REACTION

1. G. N. Watson, “Trinity College in the Time of Newton,” in Greenstreet, Isaac Newton, p. 146.

2. Newton to Oldenburg, February 6, 1672, Corres I: 40. This is a correct account of the Magnus effect, named after Heinrich Gustav Magnus, who “discovered” it in 1852, 180 years after Newton.

5. Thomas Kuhn lists Seneca (first century), Witelo (thirteenth century), Descartes, Marcus, Boyle, and Grimaldi, as well as Hooke, among those who had seen “the celebrated phenomena of colors.” “Newton’s Optical Papers,” in Cohen, Papers and Letters, p. 29. Much scholarship considers the question of when and where Newton obtained his prisms and, for that matter, when and where he first conducted this experiment. Various pieces of evidence, including this letter, the Fitzwilliam Notebook and the recollections of Conduitt fifty years later, contradict one another.

9. For that matter, the letter was the first major scientific work published in a journal.

10. Newton to Oldenburg, February 6, 1672, Corres I: 40, pp. 96–97 and n. 19.

11. And: “How doth the formost weake pulse keepe pace with the following stronger?” Add MS 3958(3).1, notes “Out of Mr Hooks Micrographia.”

13. As Kuhn notes: “To destroy the modification theory it was necessary to notice a quantitative discrepancy between the elongation predicted by that theory and the elongation actually observed, and this required an experimenter with a knowledge of the mathematical law governing refraction (not announced until 1637) and with considerable experience in applying the law to optical problems. In 1666 these qualifications were uniquely Newton’s.” “Newton’s Optical Papers,” in Cohen, ed., Papers and Letters, p. 32.

14. Casper Hakfoort, “Newton’s Optics: The Changing Spectrum of Science,” in Fauvel et al., p. 84.

17. Hooke to Oldenburg, February 15, 1672, Corres I: 44. Newton retorted that Hooke might as well speak of the “light in a piece of wood before it be set on fire.” Newton to Oldenburg, June 11, 1672, Corres I: 67.

19. Newton to Oldenburg, April 13, 1672, Corres I: 55. Pardies replied politely that Newton had answered some of his objections and that hypothesis had merely been the first word that came to mind.

20. He continued: “I shall now take a view of Mr Hooks Considerations on my Theories. And those consist in ascribing an Hypothesis to me which is not mine … & in denying some thing the truth of which would have appeared by an experimentall examination.” Newton to Oldenburg, June 11, 1672, Corres I: 67.

22. Newton to Oldenburg, March 8, 1673, Corres I: 101; Newton to Collins, May 20, 1673, Corres I: 110. Oldenburg to Newton, June 4, 1673, Corres I: 112.

23. “… or rather that you will favour me in my determination by preventing so far as you can conveniently any objections or other philosophicall letters that may concern me.” Newton to Oldenburg, June 23, 1673, Corres I: 116.

24. Newton’s silence lasted from June 1673 to November 1675—broken only by one more curt rejection: “I have long since determined to concern my self no further about the promotion of Philosophy. And for the same reason I must desire to be excused from ingaging to exhibit yearly philosophic discourses.… If it were my lot to be in London for sometime, I might possible take occasion to supply a vacant week or two with something by me, but that’s not worth mentioning.” Newton to Oldenburg, December 5, 1674, Corres I: 129.

25. “umbram captando eatinus perdideram quietam meam.…” Newton to Oldenburg, October 24, 1676, Corres II: 188.

8: IN THE MIDST OF A WHIRLWIND

1. Boyle, The Sceptical Chymist, p.57. Yet he did not quite believe that gold was an element, in the modern sense.

3. The various alternative versions of the Hypothesis are best seen in the Correspondence: Newton to Oldenburg, December 7, 1675, Corres I: 146.

5. It included, besides the “Hypothesis” (not published during his lifetime), the “Note on the Discourse of Observations” (adapted almost intact, decades later, as Book II of the Opticks).

6. Overoptimistic by a factor of a thousand or so. Corres I: 391 n.; Birch, History of the Royal Society, III: 303; S. I. Vavilov, “Newton and the Atomic Theory,” in Royal Society, Newton Tercentenary Celebrations, p. 48.

9. Newton’s physical intuition failed him here, in that he neglected another source of damping for a pendulum in vacuum—friction within the cord—but years later, soon before the Principia, he repeated this experiment more carefully and began to lose faith in the ether. Cf. Westfall, “Uneasily Fitful Reflections on Fits of Easy Transmission,” in Palter, Annus Mirabilis, pp. 93 and 100 n.; also “De Ære et Æthere,” Add MS 3970.

11. “And they that will,” he added, “may also suppose, that this Spirit affords or carryes with it thither the solary fewell & materiall Principle of Light; And that the vast æthereall Spaces between us, & the stars are for a sufficient repository for this food of the Sunn & Planets.” Corres I: 366.

15. Hooke and Oldenburg were at war over another matter, Oldenburg’s promotion of Huygens’s invention of a spiral-spring-regulated watch—previously invented, according to Hooke, by Hooke. Hooke’s extant diary scarcely mentions Newton, ever, but Oldenburg is everpresent: e.g., “the Lying Dog Oldenburg”; “Oldenburg treacherous and a villain.” Hooke, Diary, November 8, 1675 and January 28, 1673; ’Espinasse, Robert Hooke, pp. 9 and 65.

16. “These to my much esteemed friend, Mr Isaack Newton, at his chambers in Trinity College.…” Hooke to Newton, January 20, 1676, Corres I: 152.

18. Some commentators have been pleased to note that, in literal terms, Hooke was no giant; his physique was diminutive and twisted. His contemporary John Aubrey described him in Brief Lives as “but of midling stature, something crooked, pale faced, and his face but little belowe, but his head is lardge.” This hardly seems relevant to Newton’s choice of trope. It is clear that the shoulders of giants had already lived for some centuries as a conventional expression; Robert Merton has traced its course most magisterially.

9: ALL THINGS ARE CORRUPTIBLE

1. An “oven mouthed chimney.” Yehuda MS 34, quoted in Westfall, Never at Rest, p.253 n.

2. Stukeley, Memoirs, pp. 60–61; Humphrey Newton’s recollection, Keynes MS 135; John Wickins, Keynes MS 137.

3. Analysis of four surviving locks of Newton’s hair in 1979 found toxic levels of mercury. Johnson and Wolbarsht, “Mercury Poisoning: A Probable Cause of Isaac Newton’s Physical and Mental Ills”; Spargo and Pounds, “Newton’s ‘Derangement of the Intellect.’ ” But the severity remains in doubt, as do suggestions that mercury poisoning contributed to Newton’s mental troubles. See also Ditchburn, “Newton’s Illness of 1692–3.”

5. Keynes MS 33. Maybe Mr. F. was Ezekial Foxcroft (Dobbs, Foundations of Newton’s Alchemy, p. 112); at any rate the mystery, and the peopling of his papers with unidentified gentlemen, is a continual source of frustration for his biographers. “This is only speculation, of course,” Westfall remarks, typically. “It is not speculation that Newton had alchemical manuscripts which he must have received from someone since they did not, I believe, materialize out of thin air.” Westfall, Never at Rest, p. 290.

6. In the 1680s he had an amanuensis, Humphrey Newton (no relation), who recalled: “Especially at the Spring and Fall of the Leaf, at which Times he used to imploy about 6 weeks in his Elaboratory, the Fire scarcely going out either Night or Day, he siting up one Night, as I did another, till he had finished his Chymical experiments.… What his Aim might be, I was not able to penetrate into, but his Pains … made me think, he aimed at something beyond the Reach of humane Art and Industry.” Cohen and Westfall, Newton: Texts, p. 300.

7. The Works of Geber Englished by Richard Russell (reprinted London: Dent, 1928), p. 98.

8. Cinnabar was red mercuric sulfide, also known to painters as vermilion. Alchemists knew that it was a “sublimation” of quicksilver (mercury) and brimstone (sulfur). Meanwhile, the identification of quicksilver with mercury was not perfect; alchemists also spoke of a “philosophic mercury,” a more general substance, which might be extracted from other metals as well.

10. The symbol was a pair of serpents—one male and one female—entwined about a staff.

14. “In my simple judgment the noble Author since he has thought fit to reveale himself so far does prudently in being reserved in the rest.” Newton to Oldenburg, April 26, 1676, Corres II: 157. Newton concludes with regret for his unusual loquacity: “I have been so free as to shoot my bolt: but pray keep this letter private to your self.”

15. Peter Spargo, “Newton’s Chemical Experiments,” in Theerman and Seeff, Action and Reaction, p. 132: “To the best of my knowledge no contemporary chemist, including Boyle, approached this degree of quantification in chemistry—nor indeed was anyone to do so until some time later.”

16. “On Natures Obvious Laws and Processes in Vegetation,” in Cohen and Westfall, Newton: Texts, pp. 301, 305, and 303.

19. “De Gravitatione et æquipondio fluidorum,” in Hall and Hall, Unpublished Scientific Papers, p. 151. “I suppose that the parts of hard bodies do not merely touch each other and remain at relative rest, but that they do so besides so strongly and firmly cohere, and are so bound together, as it were by glue.…”

20. “And what certainty can there be in Philosophy which consists in as many Hypotheses as there are Phænomena to be explained.” Add MS 3970.3, quoted in Hutchison, “What Happened to Occult Qualities in the Scientific Revolution?”

10: HERESY, BLASPHEMY, IDOLATRY

1. Westfall, Never at Rest, pp. 311–12. The “theological notebook” is Keynes MS 2, one of those marked (by Thomas Pellett) after Newton’s death “Not fit to be printed” and then stored, unread, until Keynes acquired it in 1936.

2. He told Oldenburg and reminded him in January 1675: “the time draws near that I am to part with my fellowship.…” Corres VII: X.132.

3. From a memorandum by David Gregory, in Cohen and Westfall, Newton: Texts, p. 329.

4. “The father is immoveable no place being capable of becoming emptier or fuller ofhim then it is by the eternal necessity of nature: all other being are moveable from place to place.” “A Short Schem of the True Religion,” Keynes MS 7, in Cohen and Westfall, Newton: Texts, p. 348.

6. “Religion is partly fundamental and immutable, partly circumstantial and mutable.” “A Short Schem of the True Religion,” Keynes MS 7, in Cohen and Westfall, Newton: Texts, p. 344.

8. Scholars agree that no ancient Greek texts include the phrase these three are one. Modern English translations have instead (typically) the three are in agreement.

10. Quoted in Dobbs, Foundations of Newton’s Alchemy, p. 164. Also Jan Golinski, “The Secret Life of an Alchemist,” in Fauvel et al., Let Newton Be!

11. By the end of his life, a few people knew, including William Whiston, his successor as Lucasian Professor at Cambridge. Whiston was stripped of the professorship and tried for heresy because he made his own Arianism public. He had received the post because of Newton’s patronage; then Newton refused him membership in the Royal Society because—Whiston believed—“they durst not choose a Heretick.” Whiston said of his patron, “He was of the most fearful, cautious, and suspicious temper, that I ever knew.” Memoirs, pp. 250 f.
Westfall notes (Never at Rest, p. 318) that Isaac Barrow had gone so far as to write a “Defense of the Blessed Trinity,” and his successor as Master of Trinity College vowed to “batter the atheists and then the Arians.…”
By the time of his death, rumors of Newton’s Arianism had circulated, but his friends and then his biographers heartily denied them. E.g., Stukeley (Memoirs, p. 71): “Several people of heretical and unsettled notions, particularly those of Arian principles, have taken great pains to inlist Sir Isaac into their party, but that with as little justice as the anti-christians.”

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

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

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).

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.

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.

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.

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.

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.

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.

12: EVERY BODY PERSEVERES

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.

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

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.

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

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.

27. Add MS 3965, “De motu corporum,” in Hall and Hall, Unpublished Scientific Papers, p. 281.

28. Principia 875–78 and 839. There was nothing conclusive in this data, but Newton did not pass it by. He did not restrict himself to idealized tides but tried to consider the geography of estuaries and rivers. He studied the map of Batsha Harbor, with multiple inlets and open channels, reaching the China Sea and the Indian Ocean, and worked out a theory of wave interference that could account for the data. I. Bernard Cohen, “Prop. 24: Theory of the Tides; The First Enunciation of the Principle of Interference,” in Principia 240; Ronan, Edmond Halley, pp. 69f.

30. These explicitly became rules in the second edition; in the first, they were called “hypotheses.” Principia 794–96. There were four rules in all; the others were:

Those qualities of bodies that cannot be increased or diminished and that belong to all bodies on which experiments can be made should be taken as qualities of all bodies universally.

In experimental philosophy, propositions gathered from phenomena by induction should be considered either exactly or very nearly true notwithstanding any contrary hypotheses, until yet other phenomena make such propositions either more exact or liable to exceptions.

32. “I do not feign hypotheses” is the most popular solution to one of history’s most debated translation problems: “Hypotheses non fingo.” A reasonable alternative is “frame.” Either way, Newton always gets credit for this phrase, but he did not invent it. Henry Oldenburg (for example) had described the Royal Society’s virtuosi as those “who, neither feigning nor formulating hypotheses of nature’s actions, seek out the thing itself.” Oldenburg to Francisco Travagino, May 15, 1667.

13: IS HE LIKE OTHER MEN?

1. “Aphorisms Concerning the Interpretation of Nature and the Kingdom of Man,” Bacon, Novum Organum, p. 43.

2. “This incomparable Author having at length been prevailed upon to appear in publick, has in this Treatise given a most notable instance of the extent of the powers of the Mind.…” Phil. Trans. 186: 291.

3. Halley to King James II, July 1687, Corres II: 310. Whatever James did with his copy, it did not survive.

4. Halley, “The true Theory of the Tides, extracted from that admired Treatise of Mr. Isaac Newton, Intituled, Philosophiæ Naturalis Principia Mathematica,” Phil. Trans. 226: 445, 447.

8. Newton to a Friend, November 14, 1690, Corres III: 358. “Yes truly those Arians were crafty Knaves that could conspire so cunningly & slyly all over the world at once.”

9. Pepys to Newton, November 22, 1693, Corres III: 431. Pepys was more interested than most in arithmetical matters; he had learned multiplication at the age of twenty-nine with the help of a ship’s mate. Thomas, “Numeracy in Early Modern England,” pp. 111-12.

13. Bibliothèque Universelle et Historique (March 1688, probably by Locke himself), Acta Eruditorum (June 1688), and Journal des Sçavans (August 1688).

16. Draft of the General Scholium (section IV, no. 8, MS C), in Hall and Hall, Unpublished Scientific Papers, p. 90.

19. “The Rise of the Apostasy in Point of Religion,” Yehuda MS 18, Jewish National and University Library, Jerusalem.

20. The particulars of Newton’s breakdown will forever inspire debate and speculation. As for the fire, most believe Newton lost some papers to fire in the late seventies; Westfall goes further and suggests, “There may … have been a fire—another fire, as it appears to me—which could well have distracted him when he was already in a state of acute tension. Charred papers survive from the 1690s, though it is difficult to fit them.…” Never at Rest, p. 538. A popular legend involving a dog called Diamond and a candle (cf. Bartlett’s Familiar Quotations) is surely apocryphal. As for the involuntary restraint: no. As for mercury poisoning: he did suffer symptoms such as insomnia and apparent paranoia, but he lacked others, and these were temporary; modern tests of his hair did reveal toxic mercury levels, but the hair cannot be dated. Some of the debate plays out in Spargo and Pounds, “Newton’s ‘Derangement of the Intellect’ ”; Johnson and Wolbarsht, “Mercury Poisoning: A Probable Cause of Isaac Newton’s Physical and Mental Ills”; Ditchburn, “Newton’s Illness of 1692–3”; and Klawans, Newton’s Madness.
Whiteside has summarized the scholarly state of affairs: “Where scholars have, from the pedestals of their own stand-points, bickered ceaselessly this past century and a half over the possible causes and long-term after-effects of Newton’s undeniable breakdown … we would be foolish to attempt any definitive assessments when the extant record offers but a blurred glimpse.…” Math VII: xviii.

21. Newton to Pepys, September 13, 1693, and Newton to Locke, September 16, 1693; Corres III: 420 and 421.

24. David Gregory was the new professor of astronomy and an original proselytizer for the Principia. “David Gregory’s Inaugural Lecture at Oxford,” Notes and Records of the Royal Society 25 (1970): 143–78.

26. Oeuvres de Huygens XXI: 437, quoted in Westfall, Force in Newton’s Physics, p. 184, and cf. Guerlac, Newton on the Continent, p. 49.

29. Leibniz to Newton, March 7, 1693, Corres III: 407. It was their first contact since the brief correspondence sixteen years before.

30. Memoranda by David Gregory, Corres IV: 468, and Flamsteed’s recollection, Corres IV: 8 n.; Newton to Flamsteed, January 7, 1694, Corres IV: 473.

33. To Newton Flamsteed wrote: “I have somtimes told some ingenious men that more time and observations are required to perfect the Theory but I found it was represented as a little peice of detraction which I hate.… I wonder that hints shoud drop from your pen, as if you Lookt on my business as trifling.” January 10, 1699, Corres IV: 604.

34. Nicholas Kollerstrom’s computer-assisted analysis, Newton’s Forgotten Lunar Theory, is definitive. Kollerstrom judges the method, as employed by Halley, as accurate enough to have won a £10,000 prize established by Parliament in 1714.

35. Westfall, Never at Rest, p. 550. He did retain his professorship and salary, but he seldom visited Cambridge again, and “as far as we know, he wrote not a single letter back to any acquaintance made during his stay.”

14: NO MAN IS A WITNESS IN HIS OWN CAUSE

2. The problem was to find the curve (the brachistochrone) along which a body descending to a given point under its own gravity will take the shortest time. (Roughly: the shape of the fastest track for a roller coaster.) Galileo had thought the curve of fastest descent would be a simple arc of a circle, which is certainly faster than a straight-line ramp. In fact it is the curve known as the cycloid.
Bernoulli had posed the problem with Newton in mind, as a challenge, in the context of the simmering calculus priority dispute. He addressed it to “the very mathematicians who pride themselves that … they have not only penetrated most intimately the hiding-places of a more secret Geometry, but have even extended its limits in a remarkable way by their golden theorems” (quoted by Mandelbrote, Footprints of the Lion, p. 76). Newton solved it the night it arrived, and to Whiteside (“Newton the Mathematician,” in Bechler, Contemporary Newtonian Research, p. 122) this feat was evidence of the deterioration of his mathematical powers in old age: “A couple of years earlier his method of ‘maxima & minima in infinitesimals’ would have detected that this is the cycloid in a few minutes, not the twelve hours he in his rustiness then took.”

6. “… thou hast ordered all things in measure and number and weight.” Wisdom of Solomon 11: 20.

8. Newton upon becoming Warden was obliged to swear an oath: “You will not reveal or discover to any person or persons whatsoever the new Invention of Rounding the money & making the edges of them with letters or grainings or either of them directly or indirectly. So help you God.” Corres IV: 548.

9. “… only 400lib per annum with a house of 40lib per annum & his perquisites are only 3lib 12s per annum … so small … not to support the authority of the office.” Corres IV: 551.

10. On the matter of Newton and crimson, no one has been more eloquent than Richard de Villamil in 1931 (Newton the Man, pp. 14–15), after analyzing his household inventory:

… crimson mohairs nearly everywhere. Newton’s own bed was a “crimson mohair bed,” with “crimson Harrateen’ bed-curtains” … “crimson mohair hangings” … a “crimson sattee.” In fact, there is no other colour referred to in the “Inventary” but crimson. This living in what I may call an “atmosphere of crimson” is probably one of the reasons why Newton became rather irritable toward the end of his life.

11. Newtonians struggled with euphemisms for this relationship even into the twentieth century (“about the exact nature of [their] friendship there has been unseemly speculation,” wrote Andrade in 1947). When Halifax died, in 1715, he left Barton a bequest of more than £20,000—“for her excellent conversation,” Flamsteed wrote maliciously. There was gossip (though this mangled the sequence of events) that the connection had facilitated Newton’s appointment to the Mint; Voltaire spread it most famously: “The infinitesimal calculus and gravitation would have been of no use without a pretty niece” (Lettres Philosophiques, letter 21).
Then again, Newton’s Freudian biographer Frank Manuel avoided euphemism altogether, choosing to view Catherine as an incarnation of Hannah: “In the act of fornication between his friend Halifax and his niece was Newton vicariously having carnal intercourse with his mother?” Manuel, Portrait, p. 262.

13. China, for example, placed a higher value on silver than Europe did, and arbitrage ensued. “Our silver must go to China till gold is dearer there or cheaper with us,” Newton wrote. “The trade for their gold must greatly increase our coin, being a profit to the nation.…” Craig, Newton at the Mint, p. 43.

16. Signed, “Your near murderd humble Servant W. Chaloner.” Chaloner to Newton, March 6, 1699, Corres IV: 608.

17. Memorandum, “Of the assaying of Gold and Silver, the making of indented Triall-pieces, and trying the moneys in the Pix,” Mint Papers (Public Record Office, Kew), I: f. 109. “A Scheme of a Commission for prosecuting Counterfeiters & Diminishers of the current coyn,” manuscript, Pierpont Morgan Library.

19. Wallis to Newton, Corres IV: 503 and 567. Wallis added, “I should say the same about many things you keep hidden, of which I am not yet aware.”

21. A Latin version of the Opticks appeared two years later, in 1706—long before the first English version of the Principia, in 1729.

24. These are still called Newton’s rings. Nevertheless, reluctant though Newton was to admit it, the origins of this investigation lay in Hooke’s Micrographia.

25. Opticks, book II, part 3, proposition XIII, p. 280. Cf. Westfall, “Uneasily Fitful Reflections on Fits of Easy Transmission,” in Palter, Annus Mirabilis, pp. 88–104.

26. E.g., Opticks, p. 376. Newton’s grandest metaphysical speculation—particularly the credo of Query 31—did not appear full-blown in the first edition, but evolved, beginning with the Latin edition of 1706.

29. Francis Hauksbee, a former assistant of Robert Boyle, and then John Theophilus Desaguliers, later a renowned popularizer of Newton in prose and verse.

33. The first French translation did not appear until 1720. Even so this preceded by thirty-six years the first—and only—French translation of the Principia, by Gabrielle-Émilie Le Tonnelier de Breteuil, Marquise du Châtelet, Voltaire’s friend and lover (“she was a great man whose only fault was in being a woman”). Her name, and not Newton’s, appeared on the title page. It was Châtelet who said of Cartesianism: “It is a house collapsing into ruins, propped up on every side.… I think it would be prudent to leave.”

35. “I have even noticed certain things from which it appears that Dynamics, or the law of forces, are not deeply explored by him.” Leibniz to J. Bernoulli, March 29, 1715, Corres IV: 1138. Newton was well, if belatedly, aware of the danger of sensorium, and he backtracked in revising this passage.

36. Alexander, Leibniz-Clarke Correspondence, p. 30. Howard Stein suggests that if Leibniz had understood the “incoherence” of his relativism, he would have been better equipped to appreciate gravitation. “Newton’s Metaphysics,” in Cohen and Smith, Cambridge Companion to Newton, p. 300.

37. The so-called Epistola Posterior, Newton to Oldenburg, October 24, 1676, Corres II: 188. Cf. Principia 651 n. The key is in Add MS 4004.

38. “… which without our differential calculus no one could attack with such ease.” Acta Eruditorum, May 1684, trans. D. J. Struik, in Fauvel and Gray, History of Mathematics, p. 434.

39. Newton’s letters to Leibniz first appeared in John Wallis’s third volume of Opera Mathematica in 1699—a deliberate marshaling of evidence. Barrow had sent Collins Newton’s De Analysi per Æquationes Infinitas in 1669, and Collins, before returning it, had made at least one copy—which he showed Leibniz in 1676,

40. John Keill, Phil. Trans. 26 (1709), quoted by Westfall, Never at Rest, p. 715.

42. “An Account of the Book Entituled Commercium Epistolicum, Collinii et Aliorum, de Analysi Promota,” Phil. Trans. 342 (February 1715): 221.

46. As L. J. Russell put it: “You might at any moment hit on a simple substitution, e.g. in an algebraic equation, or in a summation of a series, that would lead to a new general method.… Sometimes even the hint that someone had discovered a method for solving a particular problem was enough to set you looking in the right direction for solving it, and you could solve it too. In such a situation, what is needed is a general clearing house of publicity.” “Plagiarism in the Seventeenth Century, and Leibniz,” in Greenstreet, Isaac Newton, p. 135.

47. Leibniz’s symbols did not map neatly onto the notation Newton had devised for his own use, dotted letters for fluxions and various alternatives for fluents, and the consequence was that British and Continental mathematics diverged throughout the eighteenth century. Finally, in the nineteenth, Leibniz’s differential notation prevailed over the dots even in England.

48. Lenore Feigenbaum, “The Fragmentation of the European Mathematical Community,” in Harman and Shapiro, Investigation of Difficult Things, p. 384. She also quotes Whiteside, calling the controversy “a long-festering boil [that] polluted the whole European world for a decade afterwards with the corruption of its discharging pus.” Math VIII: 469.

49. Baily, Account of the Revd John Flamsteed, p. 294. Flamsteed died soon after, having been Royal Astronomer forty-five years, and Halley took his place.

51. Leibniz to Rémond de Montmort, October 19, 1716, quoted in Manuel, Portrait, p. 333.

15: THE MARBLE INDEX OF A MIND

4. Letters on England, pp. 86 and 79–80. For a generation to come, Anglo-French rivalry colored Newton’s reception in France. He had been elected a foreign member of the Académie Royale in 1699 but had never acknowledged the honor or communicated with the academy. When French scientists meant “Newtonians,” they generally said, “les anglais.”

5. Bernard le Bovier de Fontenelle, The Eloguim of Sir Isaac Newton (London: Tonson, 1728), read to the Académie Royale des Sciences in November 1727; reprinted in Cohen, ed., Papers and Letters, pp. 444–74; based in turn on John Conduitt’s “Memoir,” in Isaac Newton: Eighteenth-Century Perspectives, pp. 26–34. (“He had such a meekness and sweetness of temper.… His whole life was one continued series of labour, patience, charity, generosity, temperance, piety, goodness, and all other virtues, without a mixture of any vice whatsoever.”) In the contemporary manner, Fontenelle also embellished Newton’s ancestry: “descended from the elder branch of the family of Sir John Newton Baronet.… Manor of Woolstrope had been in his Family near 200 years.… Sir Isaac’s Mother … was likewise of an ancient family.…” In fairness to Fontenelle, he relied on a pedigree Newton had embellished himself, after being knighted.
The supposedly singular laugh is originally due to Humphrey Newton; Stukeley (Memoirs, p. 57) considered this at length and said that he had often seen Newton laugh and that “he was easily made to smile, if not to laugh.”

7. “… Nature her self to him resigns the Field,/ From him her Secrets are no more conceal’d.” Gentleman’s Magazine I (February 1731): 64.

9. Epitaphs (1730). Here Pope was serving a long, slow pitch to the twentieth century wag who replied: “It did not last: the Devil howling ‘Ho, / Let Einstein be,’ restored the status quo.” Koyré, “The Newtonian Synthesis,” in Newtonian Studies.

10. One of the observers, William Whiston, said he made enough money from eclipse lectures and “the sale of my schemes before and after” to support his family for a year, and added: “There happened to be a Mahometan envoy here from Tripoly, who at first thought we were distracted, by pretending to know so very punctually when God Almighty would totally eclipse the Sun; which his own musselmen were not able to do.… When the eclipse came exactly as we foretold, he was asked again, what he thought of the matter now? His answer was, that he supposed we knew this by art magick.” Memoirs, p. 205.

12. Not till 1890, if we believe the OED, and its first appearance was pejorative: “1890 Athenæum 19 July 92/2 [Mercier] declared Newtonianism to be the ‘most absurd scientific extravagance that has ever issued from the human imagination.’ ”

13. Sir Isaac Newton’s Philosophy Explain’d for the Use of the Ladies (London: E. Cave, 1739), p. 231.

15. Haydon’s Autobiography (1853), quoted in Nicolson, Newton Demands the Muse, p. 1; and Penelope Hughes-Hallett, The Immortal Dinner: A Famous Evening of Genius and Laughter in Literary London, 1817 (London: Viking, 2000).

17. Shelley, Queen Mab, V: 143–45. He read Newton carefully and with understanding. “We see a variety of bodies possessing a variety of powers: we merely know their effects; we are in a state of ignorance with respect to their essences and causes. These Newton calls the phenomena of things; but the pride of philosophy is unwilling to admit its ignorance of their causes.” Notes to Queen Mab, VII.

21. Blake, “On the Virginity of the Virgin Mary & Johanna Southcott” (Satiric Verses & Epigrams). Also: “To teach doubt & Experiment / Certainly was not what Christ meant.” The Everlasting Gospel.

27. As Clifford Truesdell puts it (“Reactions of Late Baroque Mechanics to Success, Conjecture, Error, and Failure in Newton’s Principia,” in Palter, Annus Mirabilis, p. 192): “Newton relinquished the diplomatic immunity granted to nonmathematical philosophers, chemists, psychologists, etc., and entered into the area where an error is an error even if it is Newton’s error; in fact, all the more so because it is Newton’s error.”

29. Steven Weinberg, “The Non-Revolution of Thomas Kuhn,” in Facing Up, p. 197: “Kuhn knew very well that physicists today go on using the Newtonian theory of gravitation and motion.… We certainly don’t regard Newtonian and Maxwellian theories as simply false, in the way that Aristotle’s theory of motion or the theory that fire is an element are false.”

32. Einstein’s space-time was not, therefore, that of Leibniz and other contemporary anti-Newtonians. As H. G. Alexander notes, Leibniz’s critique of absolute space and time in no way anticipated Einstein’s: “Leibniz’s fundamental postulate is that space and time are unreal. No one therefore would have rejected more strongly than he a theory which ascribes properties to space-time.” The Leibniz-Clarke Correspondence, Introduction, p. lv. Or, as Howard Stein puts it: “In spite of the fact that absolute space and absolute time have been abandoned, and the geometric structure of space-time has proved to be interdependent with the distribution of matter … it remains necessary to regard space-time and its geometry as having a status as ‘real’ as that of matter.… On this general score—although certainly not in detail—Newton was, in the eyes of our own science, ‘right’ to take space and time as fundamental entities.” “Newton’s Metaphysics,” in Cohen and Smith, Cambridge Companion to Newton, p. 292.

33. Einstein, “What Is the Theory of Relativity?” Times of London, November 28, 1919, reprinted in Out of My Later Years, p. 58a. And as he put it a few years later (1927): “We have to realize that before Newton there existed no self-contained system of physical causality which was somehow capable of representing any of the deeper features of the empirical world.” Einstein, “The Mechanics of Newton and Their Influence on the Development of Theoretical Physics,” in Ideas and Opinions, p. 277.

38. Even here, in establishing this fundamental dictum of science, he allowed for the alternative possibility. His heirs and followers forgot, but he wrote: “it may also be allow’d that God is able to create Particles of Matter of several Sizes and Figures, and in several Proportions to Space, and perhaps of different Densities and Forces, and thereby to vary the Laws of Nature, and make Worlds of several sorts in several Parts of the Universe. At least, I see nothing of Contradiction in all this.” Opticks 403–4.

39. “Newton and the Twentieth Century—A Personal View,” in Fauvel et al., Let Newton Be!, p. 244.

40. Scott Mandelbrote says: “The causes of this are hard to fathom but may relate to the international situation, the sense that Cambridge already possessed all that mattered of Newton’s papers, fatigue in a market that was already awash with books from Newton’s library, or even disquiet at Lord Lymington’s right-wing political views.” Footprints of the Lion, p. 137.
The total sale amounted to barely £9,000, including two portraits and the death mask. Most of the interest and the pre-sale publicity came from the United States. P. E. Spargo, “Sotheby’s, Keynes, and Yahuda: The 1936 Sale of Newton’s Manuscripts,” in Harman and Shapiro, Investigation of Difficult Things, pp. 115–34.

41. John Maynard Keynes, “Newton the Man,” in Royal Society, Newton Tercentenary Celebrations, p. 27. Freeman Dyson, who was there, describes Keynes’s talk in Disturbing the Universe (New York: Harper & Row, 1979), pp. 8–9.

42. Edited by Conduitt, this became (after the Principia and Opticks) one of his first works published, the year after his death. To modern eyes it is, as Westfall declared plaintively, “a work of colossal tedium … read today only by the tiniest remnant who for their sins must pass through its purgatory.” Westfall, Never at Rest, p.815.

44. “Principles of Philosophy,” manuscript fragment (c. 1703), Add MS 3970.3

46. Inventory, “Dom Isaaci Newton, Mil.,” dated May 5, 1727, in de Villamil, Newton the Man, pp. 49–61.