## 1. Newton's Life




Newton's life naturally divides into four parts: the years before he
entered Trinity College, Cambridge in 1661; his years in Cambridge
before the *Principia* was published in 1687; a period of almost
a decade immediately following this publication, marked by the renown
it brought him and his increasing disenchantment with Cambridge; and
his final three decades in London, for most of which he was Master of
the Mint. While he remained intellectually active during his
years in London, his legendary advances date almost entirely from his
years in Cambridge. Nevertheless, save for his optical papers of
the early 1670s and the first edition of the *Principia*, all
his works published before he died fell within his years in
 London.[1]


### 1.1 Newton's Early Years




Newton was born into a Puritan family in Woolsthorpe, a small village
in Linconshire near Grantham, on 25 December 1642 (old calendar), a few
days short of one year after Galileo died. Isaac's father, a
farmer, died two months before Isaac was born. When his mother
Hannah married the 63 year old Barnabas Smith three years later and
moved to her new husband's residence, Isaac was left behind with his
maternal grandparents. (Isaac learned to read and write from his
maternal grandmother and mother, both of whom, unlike his father, were
literate.) Hannah returned to Woolsthorpe with three new children in
1653, after Smith died. Two years later Isaac went to boarding
school in Grantham, returning full time to manage the farm, not very
successfully, in 1659. Hannah's brother, who had received an M.A.
from Cambridge, and the headmaster of the Grantham school then
persuaded his mother that Isaac should prepare for the
university. After further schooling at Grantham, he entered
Trinity College in 1661, somewhat older than most of his
classmates.




These years of Newton's youth were the most turbulent in the history of
England. The English Civil War had begun in 1642, King Charles
was beheaded in 1649, Oliver Cromwell ruled as lord protector from 1653
until he died in 1658, followed by his son Richard from 1658 to 1659,
leading to the restoration of the monarchy under Charles II in
1660. How much the political turmoil of these years affected
Newton and his family is unclear, but the effect on Cambridge and other
universities was substantial, if only through unshackling them for a
period from the control of the Anglican Catholic Church. The
return of this control with the restoration was a key factor inducing
such figures as Robert Boyle to turn to Charles II for support for what
in 1660 emerged as the Royal Society of London. The intellectual
world of England at the time Newton matriculated to Cambridge was thus
very different from what it was when he was born.


### 1.2 Newton's Years at Cambridge Prior to *Principia*




Newton's initial education at Cambridge was classical, focusing
(primarily through secondary sources) on Aristotlean rhetoric, logic,
ethics, and physics. By 1664, Newton had begun reaching beyond the
standard curriculum, reading, for example, the 1656 Latin edition of
Descartes's *Opera philosophica*, which included the
*Meditations*, *Discourse on Method*, the
*Dioptrics*, and the *Principles of Philosophy*. By
early 1664 he had also begun teaching himself mathematics, taking
notes on works by Oughtred, Viete, Wallis, and Descartes
-- the latter via van Schooten's Latin translation, with
commentary, of the *Geometrie*. Newton spent all
but three months from the summer of 1665 until the spring of 1667 at
home in Woolsthorpe when the university was closed because of the
plague. This period was his so-called *annus
mirabilis*. During it, he made his initial experimental
discoveries in optics and developed (independently of Huygens's
treatment of 1659) the mathematical theory of uniform circular motion,
in the process noting the relationship between the inverse-square and
Kepler's rule relating the square of the planetary periods to the cube
of their mean distance from the Sun. Even more impressively, by late
1666 he had become *de facto* the leading mathematician in the
world, having extended his earlier examination of cutting-edge
problems into the discovery of the calculus, as presented in his tract
of October 1666. He returned to Trinity as a Fellow in 1667, where he
continued his research in optics, constructing his first reflecting
telescope in 1669, and wrote a more extended tract on the calculus
"De Analysi per AEquations Numero Terminorum
Infinitas" incorporating new work on infinite series. On the
basis of this tract Isaac Barrow recommended Newton as his replacement
as Lucasian Professor of Mathematics, a position he assumed in October
1669, four and a half years after he had received his Bachelor of
Arts.




Over the course of the next fifteen years as Lucasian Professor Newton
presented his lectures and carried on research in a variety of
areas. By 1671 he had completed most of a treatise length account
of the
 calculus,[2]
which he then found no one would publish. This failure appears to have
diverted his interest in mathematics away from the calculus for some
time, for the mathematical lectures he registered during this period
mostly concern algebra. (During the early 1680s he undertook a
critical review of classical texts in geometry, a review that reduced
his view of the importance of symbolic mathematics.) His lectures
from 1670 to 1672 concerned optics, with a large range of experiments
presented in detail. Newton went public with his work in optics in
early 1672, submitting material that was read before the Royal Society
and then published in the *Philosophical Transactions of the Royal
Society*. This led to four years of exchanges with various figures
who challenged his claims, including both Robert Hooke and Christiaan
Huygens -- exchanges that at times exasperated Newton to the
point that he chose to withdraw from further public exchanges in
natural philosophy. Before he largely isolated himself in the late
1670s, however, he had also engaged in a series of sometimes long
exchanges in the mid 1670s, most notably with John Collins (who had a
copy of "De Analysi") and Leibniz, concerning his work on
the calculus. So, though they remained unpublished, Newton's advances
in mathematics scarcely remained a secret.




This period as Lucasian Professor also marked the beginning of his more
private researches in alchemy and theology. Newton purchased
chemical apparatus and treatises in alchemy in 1669, with experiments
in chemistry extending across this entire period. The issue of
the vows Newton might have to take in conjunction with the Lucasian
Professorship also appears to have precipitated his study of the
doctrine of the Trinity, which opened the way to his questioning the
validity of a good deal more doctrine central to the Roman and Anglican
Churches.




Newton showed little interest in orbital astronomy during this period
until Hooke initiated a brief correspondence with him in an effort to
solicit material for the Royal Society at the end of November 1679,
shortly after Newton had returned to Cambridge following the death of
his mother. Among the several problems Hooke proposed to Newton
was the question of the trajectory of a body under an inverse-square
central force:



> 
> 
> It now remaines to know the proprietys of a curve Line (not circular
> nor concentricall) made by a centrall attractive power which makes the
> velocitys of Descent from the tangent Line or equall straight motion at
> all Distances in a Duplicate proportion to the Distances Reciprocally
> taken. I doubt not but that by your excellent method you will
> easily find out what the Curve must be, and it proprietys, and suggest
> a physicall Reason of this
>  proportion.[3]




Newton apparently discovered the systematic relationship between
conic-section trajectories and inverse-square central forces at the
time, but did not communicate it to anyone, and for reasons that
remain unclear did not follow up this discovery until Halley, during a
visit in the summer of 1684, put the same question to him. His
immediate answer was, an ellipse; and when he was unable to produce
the paper on which he had made this determination, he agreed to
forward an account to Halley in London. Newton fulfilled this
commitment in November by sending Halley a nine-folio-page
manuscript, "De Motu Corporum in Gyrum" ("On the
Motion of Bodies in Orbit"), which was entered into the Register
of the Royal Society in early December 1684. The body of this tract
consists of ten deduced propositions -- three theorems and seven
problems -- all of which, along with their corollaries, recur in
important propositions in the *Principia*.




Save for a few weeks away from Cambridge, from late 1684 until early
1687, Newton concentrated on lines of research that expanded the short
ten-proposition tract into the 500 page *Principia*, with its
192 derived propositions. Initially the work was to have a two
book structure, but Newton subsequently shifted to three books, and
replaced the original version of the final book with one more
mathematically demanding. The manuscript for Book 1 was sent to
London in the spring of 1686, and the manuscripts for Books 2 and 3, in
March and April 1687, respectively. The roughly three hundred
copies of the *Principia* came off the press in the summer of
1687, thrusting the 44 year old Newton into the forefront of natural
philosophy and forever ending his life of comparative isolation.


### 1.3 Newton's Final Years at Cambridge




The years between the publication of the *Principia* and
Newton's permanent move to London in 1696 were marked by his
increasing disenchantment with his situation in Cambridge. In January
1689, following the Glorious Revolution at the end of 1688, he was
elected to represent Cambridge University in the Convention
Parliament, which he did until January 1690. During this time he
formed friendships with John Locke and Nicolas Fatio de Duillier, and
in the summer of 1689 he finally met Christiaan Huygens face to face
for two extended discussions. Perhaps because of disappointment with
Huygens not being convinced by the argument for universal gravity, in
the early 1690s Newton initiated a radical rewriting of the
*Principia*. During these same years he wrote (but withheld)
his principal treatise in alchemy, *Praxis*; he corresponded
with Richard Bentley on religion and allowed Locke to read some of his
writings on the subject; he once again entered into an effort to put
his work on the calculus in a form suitable for publication; and he
carried out experiments on diffraction with the intent of completing
his *Opticks*, only to withhold the manuscript from publication
because of dissatisfaction with its treatment of diffraction. The
radical revision of the *Principia* became abandoned by 1693,
during the middle of which Newton suffered, by his own testimony, what
in more recent times would be called a nervous breakdown. In the two
years following his recovery that autumn, he continued his experiments
in chymistry and he put substantial effort into trying to refine and
extend the gravity-based theory of the lunar orbit in the
*Principia*, but with less success than he had hoped.




Throughout these years Newton showed interest in a position of
significance in London, but again with less success than he had hoped
until he accepted the relatively minor position of Warden of the Mint
in early 1696, a position he held until he became Master of the Mint at
the end of 1699. He again represented Cambridge University in
Parliament for 16 months, beginning in 1701, the year in which he
resigned his Fellowship at Trinity College and the Lucasian
Professorship. He was elected President of the Royal Society in
1703 and was knighted by Queen Anne in 1705.


### 1.4 Newton's Years in London and His Final Years




Newton thus became a figure of imminent authority in London over the
rest of his life, in face-to-face contact with individuals of power and
importance in ways that he had not known in his Cambridge years.
His everyday home life changed no less dramatically when his
extraordinarily vivacious teenage niece, Catherine Barton, the daughter
of his half-sister Hannah, moved in with him shortly after he moved to
London, staying until she married John Conduitt in 1717, and after that
remaining in close contact. (It was through her and her husband
that Newton's papers came down to posterity.) Catherine was
socially prominent among the powerful and celebrated among the literati
for the years before she married, and her husband was among the
wealthiest men of London.




The London years saw Newton embroiled in some nasty disputes, probably
made the worse by the ways in which he took advantage of his position
of authority in the Royal Society. In the first years of his
Presidency he became involved in a dispute with John Flamsteed in which
he and Halley, long ill-disposed toward the Flamsteed, violated the
trust of the Royal Astronomer, turning him into a permanent
enemy. Ill feelings between Newton and Leibniz had been
developing below the surface from even before Huygens had died in 1695,
and they finally came to a head in 1710 when John Keill accused Leibniz
in the *Philosophical Transactions* of having plagiarized the
calculus from Newton and Leibniz, a Fellow of the Royal Society since
1673, demanded redress from the Society. The Society's 1712
published response was anything but redress. Newton not only was
a dominant figure in this response, but then published an outspoken
anonymous review of it in 1715 in the *Philosophical
Transactions*. Leibniz and his colleagues on the Continent
had never been comfortable with the *Principia* and its
implication of action at a distance. With the priority dispute
this attitude turned into one of open hostility toward Newton's theory
of gravity -- a hostility that was matched in its blindness by the
fervor of acceptance of the theory in England. The public
elements of the priority dispute had the effect of expanding a schism
between Newton and Leibniz into a schism between the English associated
with the Royal Society and the group who had been working with Leibniz
on the calculus since the 1690s, including most notably Johann
Bernoulli, and this schism in turn transformed into one between the
conduct of science and mathematics in England versus the Continent that
persisted long after Leibniz died in 1716.




Although Newton obviously had far less time available to devote to
solitary research during his London years than he had had in
Cambridge, he did not entirely cease to be productive. The first
(English) edition of his *Opticks* finally appeared in 1704,
appended to which were two mathematical treatises, his first work on
the calculus to appear in print. This edition was followed by a Latin
edition in 1706 and a second English edition in 1717, each containing
important Queries on key topics in natural philosophy beyond those in
its predecessor. Other earlier work in mathematics began to appear in
print, including a work on algebra, *Arithmetica Universalis*,
in 1707 and "De Analysi" and a tract on finite
differences, "Methodis differentialis" in 1711. The second
edition of the *Principia*, on which Newton had begun work at
the age of 66 in 1709, was published in 1713, with a third edition in
1726. Though the original plan for a radical restructuring had long
been abandoned, the fact that virtually every page of the
*Principia* received some modifications in the second edition
shows how carefully Newton, often prodded by his editor Roger Cotes,
reconsidered everything in it; and important parts were substantially
rewritten not only in response to Continental criticisms, but also
because of new data, including data from experiments on resistance
forces carried out in London. Focused effort on the third edition
began in 1723, when Newton was 80 years old, and while the revisions
are far less extensive than in the second edition, it does contain
substantive additions and modfications, and it surely has claim to
being the edition that represents his most considered views.




Newton died on 20 March 1727 at the age of 84. His
contemporaries' conception of him nevertheless continued to expand as a
consequence of various posthumous publications, including *The
Chronology of Ancient Kingdoms Amended* (1728); the work originally
intended to be the last book of the *Principia*, *The System
of the World* (1728, in both English and Latin); *Observations
upon the Prophecies of Daniel and the Apocalypse of St. John*
(1733); *A Treatise of the Method of Fluxions and Infinite
Series* (1737); *A Dissertation upon the Sacred Cubit of the
Jews* (1737), and *Four Letters from Sir Isaac Newton to Doctor
Bentley concerning Some Arguments in Proof of a Deity*
(1756). Even then, however, the works that had been published
represented only a limited fraction of the total body of papers that
had been left in the hands of Catherine and John Conduitt. The
five volume collection of Newton's works edited by Samuel Horsley
(1779-85) did not alter this situation. Through the marriage of
the Conduitts' daughter Catherine and subsequent inheritance, this body
of papers came into the possession of Lord Portsmouth, who agreed in
1872 to allow it to be reviewed by scholars at Cambridge University
(John Couch Adams, George Stokes, H. R. Luard, and G. D.
Liveing). They issued a catalogue in 1888, and the university
then retained all the papers of a scientific character. With the
notable exception of W. W. Rouse Ball, little work was done on the
scientific papers before World War II. The remaining papers were
returned to Lord Portsmouth, and then ultimately sold at auction in
1936 to various parties. Serious scholarly work on them did not
get underway until the 1970s, and much remains to be done on them.


## 2. Newton's Work and Influence




Three factors stand in the way of giving an account of Newton's work
and influence. First is the contrast between the public Newton,
consisting of publications in his lifetime and in the decade or two
following his death, and the private Newton, consisting of his
unpublished work in math and physics, his efforts in chymistry --
that is, the 17th century blend of alchemy and chemistry -- and
his writings in radical theology -- material that has become
public mostly since World War II. Only the public Newton influenced
the eighteenth and early nineteenth centuries, yet any account of
Newton himself confined to this material can at best be only
fragmentary. Second is the contrast, often shocking, between the
actual content of Newton's public writings and the positions
attributed to him by others, including most importantly his
popularizers. The term "Newtonian" refers to several
different intellectual strands unfolding in the eighteenth century,
some of them tied more closely to Voltaire, Pemberton, and Maclaurin
-- or for that matter to those who saw themselves as extending
his work, such as Clairaut, Euler, d'Alembert, Lagrange, and Laplace
-- than to Newton himself. Third is the contrast between the
enormous range of subjects to which Newton devoted his full
concentration at one time or another during the 60 years of his
intellectual career -- mathematics, optics, mechanics, astronomy,
experimental chemistry, alchemy, and theology -- and the
remarkably little information we have about what drove him or his
sense of himself. Biographers and analysts who try to piece together a
unified picture of Newton and his intellectual endeavors often end up
telling us almost as much about themselves as about Newton.




Compounding the diversity of the subjects to which Newton devoted time
are sharp contrasts in his work within each subject. Optics and
orbital mechanics both fall under what we now call physics, and even
then they were seen as tied to one another, as indicated by Descartes'
first work on the subject, *Le Monde, ou Traite de la
lumiere*. Nevertheless, two very different
"Newtonian" traditions in physics arose from Newton's
*Opticks* and *Principia*: from his *Opticks* a
tradition centered on meticulous experimentation and from his
*Principia* a tradition centered on mathematical theory. The
most important element common to these two was Newton's deep
commitment to having the empirical world serve not only as the
ultimate arbiter, but also as the sole basis for adopting provisional
theory. Throughout all of this work he displayed distrust of what was
then known as the method of hypotheses - putting forward
hypotheses that reach beyond all known phenomena and then testing them
by deducing observable conclusions from them. Newton insisted instead
on having specific phenomena decide each element of theory, with the
goal of limiting the provisional aspect of theory as much as possible
to the step of inductively generalizing from the specific
phenomena. This stance is perhaps best summarized in his fourth Rule
of Reasoning, added in the third edition of the *Principia*,
but adopted as early as his Optical Lectures of the 1670s:



> 
> 
> *In experimental philosophy, propositions gathered from phenomena
> by induction should be taken to be either exactly or very nearly true
> notwithstanding any contrary hypotheses, until yet other phenomena make
> such propositions either more exact or liable to exceptions.*
> 
> 
> 
> 
>  This rule should be followed so that arguments based on
> induction may not be nullified by hypotheses.
> 
> 
> 




Such a commitment to empirically driven science was a hallmark of
the Royal Society from its very beginnings, and one can find it in the
research of Kepler, Galileo, Huygens, and in the experimental efforts
of the Royal Academy of Paris. Newton, however, carried this
commitment further first by eschewing the method of hypotheses and
second by displaying in his *Principia* and *Opticks* how
rich a set of theoretical results can be secured through well-designed
experiments and mathematical theory designed to allow inferences from
phenomena. The success of those after him in building on these
theoretical results completed the process of transforming natural
philosophy into modern empirical science.




Newton's commitment to having phenomena decide the elements of
theory required questions to be left open when no available phenomena
could decide them. Newton contrasted himself most strongly with
Leibniz in this regard at the end of his anonymous review of the Royal
Society's report on the priority dispute over the calculus:



> 
> 
> It must be allowed that these two Gentlemen differ very much in
> Philosophy. The one proceeds upon the Evidence arising from
> Experiments and Phenomena, and stops where such Evidence is wanting;
> the other is taken up with Hypotheses, and propounds them, not to be
> examined by Experiments, but to be believed without Examination.
> The one for want of Experiments to decide the Question, doth not affirm
> whether the Cause of Gravity be Mechanical or not Mechanical; the other
> that it is a perpetual Miracle if it be not Mechanical.




Newton could have said much the same about the question of what
light consists of, waves or particles, for while he felt that the latter
was far more probable, he saw it still not decided by any experiment or
phenomenon in his lifetime. Leaving questions about the ultimate
cause of gravity and the constitution of light open was the other
factor in his work driving a wedge between natural philosophy and
empirical science.




The many other areas of Newton's intellectual endeavors made less of a
difference to eighteenth century philosophy and science. In
mathematics, Newton was the first to develop a full range of
algorithms for symbolically determining what we now call integrals and
derivatives, but he subsequently became fundamentally opposed to the
idea, championed by Leibniz, of transforming mathematics into a
discipline grounded in symbol manipulation. Newton thought the only
way of rendering limits rigorous lay in extending geometry to
incorporate them, a view that went entirely against the tide in the
development of mathematics in the eighteenth and nineteenth
ceturies. In chemistry Newton conducted a vast array of experiments,
but the experimental tradition coming out of his *Opticks*, and
not his experiments in chemistry, lay behind Lavoisier calling himself
a Newtonian; indeed, one must wonder whether Lavoisier would even have
associated his new form of chemistry with Newton had he been aware of
Newton's fascination with writings in the alchemical tradition. And
even in theology, there is Newton the anti-Trinitarian mild heretic
who was not that much more radical in his departures from Roman and
Anglican Christianity than many others at the time, and Newton, the
wild religious zealot predicting the end of the Earth, who did not
emerge to public view until quite recently.




There is surprisingly little cross-referencing of themes from one area
of Newton's endeavors to another. The common element across almost all
of them is that of a problem-solver *extraordinaire*, taking on
one problem at a time and staying with it until he had found, usually
rather promptly, a solution. All of his technical writings display
this, but so too does his unpublished manuscript reconstructing
Solomon's Temple from the biblical account of it and his posthumously
published *Chronology of the Ancient Kingdoms* in which he
attempted to infer from astronomical phenomena the dating of major
events in the Old Testament. The Newton one encounters in his writings
seems to compartmentalize his interests at any given moment. Whether
he had a unified conception of what he was up to in all his
intellectual efforts, and if so what this conception might be, has
been a continuing source of controversy among Newton scholars.




Of course, were it not for the *Principia*, there would be no
entry at all for Newton in an Encyclopedia of Philosophy. In science,
he would have been known only for the contributions he made to optics,
which, while notable, were no more so than those made by Huygens and
Grimaldi, neither of whom had much impact on philosophy; and in
mathematics, his failure to publish would have relegated his work
to not much more than a footnote to the achievements of Leibniz and
his school. Regardless of which aspect of Newton's endeavors
"Newtonian" might be applied to, the word gained its aura
from the *Principia*. But this adds still a further
complication, for the *Principia* itself was substantially
different things to different people. The press-run of the first
edition (estimated to be around 300) was too small for it to have been
read by all that many individuals. The second edition also appeared in
two pirated Amsterdam editions, and hence was much more widely
available, as was the third edition and its English (and later
French) translation. The *Principia*, however, is not an easy
book to read, so one must still ask, even of those who had access to
it, whether they read all or only portions of the book and to what
extent they grasped the full complexity of what they read. The
detailed commentary provided in the three volume Jesuit edition
(1739-42) made the work less daunting. But even then the vast majority
of those invoking the word "Newtonian" were unlikely to
have been much more conversant with the *Principia* itself than
those in the first half of the 20th century who invoked
'relativity' were likely to have read Einstein's two
special relativity papers of 1905 or his general relativity paper of
1916. An important question to ask of any philosophers commenting on
Newton is, what primary sources had they read?




The 1740s witnessed a major transformation in the standing of the
science in the *Principia*. The *Principia* itself
had left a number of loose-ends, most of them detectable by only highly
discerning readers. By 1730, however, some of these loose-ends
had been cited in Bernard le Bovier de Fontenelle's elogium
for
 Newton[4] and in
John Machin's appendix to the 1729 English translation of the
*Principia*, raising questions about just how secure Newton's
theory of gravity was, empirically. The shift on the continent began
in the 1730s when Maupertuis convinced the Royal Academy to conduct
expeditions to Lapland and Peru to determine whether Newton's claims
about the non-spherical shape of the Earth and the variation of
surface gravity with latitude are correct. Several of the loose-ends
were successfully resolved during the 1740's through such notable
advances beyond the *Principia* as Clairaut's
*Theorie de la Figure de la Terre*; the return of the
expedition from Peru; d'Alembert's 1749 rigid-body solution for the
wobble of the Earth that produces the precession of the equinoxes;
Clairaut's 1749 resolution of the factor of 2 discrepancy between
theory and observation in the mean motion of the lunar apogee, glossed
over by Newton but emphasized by Machin; and the prize-winning first
ever successful description of the motion of the Moon by Tobias Mayer
in 1753, based on a theory of this motion derived from gravity by
Euler in the early 1750s taking advantage of Clairaut's solution for
the mean motion of the apogee.




Euler was the central figure in turning the three laws of motion put
forward by Newton in the *Principia* into Newtonian
mechanics. These three laws, as Newton formulated them, apply to
"point-masses," a term Euler had put forward in his
*Mechanica* of 1736. Most of the effort of eighteenth century
mechanics was devoted to solving problems of the motion of rigid
bodies, elastic strings and bodies, and fluids, all of which require
principles beyond Newton's three laws. From the 1740s on this led to
alternative approaches to formulating a general mechanics, employing
such different principles as the conservation of *vis viva*,
the principle of least action, and d'Alembert's principle. The
"Newtonian" formulation of a general mechanics sprang from
Euler's proposal in 1750 that Newton's second law, in an *F=ma*
formulation that appears nowhere in the *Principia*, could be
applied locally within bodies and fluids to yield differential
equations for the motions of bodies, elastic and rigid, and
fluids. During the 1750s Euler developed his equations for the motion
of fluids, and in the 1760s, his equations of rigid-body
motion. What we call Newtonian mechanics was accordingly something for
which Euler was more responsible than Newton.




Although some loose-ends continued to defy resolution until much later
in the eighteenth century, by the early 1750s Newton's theory of
gravity had become the accepted basis for ongoing research among
almost everyone working in orbital astronomy. Clairaut's successful
prediction of the month of return of Halley's comet at the end of this
decade made a larger segment of the educated public aware of the
extent to which empirical grounds for doubting Newton's theory of
gravity had largely disappeared. Even so, one must still ask of anyone
outside active research in gravitational astronomy just how aware they
were of the developments from ongoing efforts when they made their
various pronouncements about the standing of the science of the
*Principia* among the community of researchers. The naivety of
these pronouncements cuts both ways: on the one hand, they often
reflected a bloated view of how secure Newton's theory was at the
time, and, on the other, they often underestimated how strong the
evidence favoring it had become. The upshot is a need to be attentive
to the question of what anyone, even including Newton himself, had in
mind when they spoke of the science of the *Principia*.




To view the seventy years of research after Newton died as merely tying
up the loose-ends of the *Principia* or as simply compiling more
evidence for his theory of gravity is to miss the whole point.
Research predicated on Newton's theory had answered a huge number
of questions about the world dating from long before it. The
motion of the Moon and the trajectories of comets were two early
examples, both of which answered such questions as how one comet
differs from another and what details make the Moon's motion so
much more complicated than that of the satellites of Jupiter and
Saturn. In the 1770s Laplace had developed a proper theory of the
tides, reaching far beyond the suggestions Newton had made in the
*Principia* by including the effects of the Earth's
rotation and the non-radial components of the gravitational forces of
the Sun and Moon, components that dominate the radial component that
Newton had singled out. In 1786 Laplace identified a large 900
year fluctuation in the motions of Jupiter and Saturn arising from
quite subtle features of their respective orbits. With this
discovery, calculation of the motion of the planets from the theory of
gravity became the basis for predicting planet positions, with
observation serving primarily to identify further forces not yet taken
into consideration in the calculation. These advances in our
understanding of planetary motion led Laplace to produce the four
principal volumes of his *Traite de mecanique
celeste* from 1799 to 1805, a work collecting in one place
all the theoretical and empirical results of the research predicated on
Newton's *Principia*. From that time forward,
Newtonian science sprang from Laplace's work, not
Newton's.




The success of the research in celestial mechanics predicated on the
*Principia* was unprecedented. Nothing of comparable scope
and accuracy had ever occurred before in empirical research of any
kind. That led to a new philosophical question: what was it about
the science of the *Principia* that enabled it to achieve what
it did? Philosophers like Locke and Berkeley began asking this
question while Newton was still alive, but it gained increasing force
as successes piled on one another over the decades after he died.
This question had a practical side, as those working in other fields
like chemistry pursued comparable success, and others like Hume and
Adam Smith aimed for a science of human affairs. It had, of
course, a philosophical side, giving rise to the subdiscipline of
philosophy of science, starting with Kant and continuing throughout the
nineteenth century as other areas of physical science began showing
similar signs of success. The Einsteinian revolution in the
beginning of the twentieth century, in which Newtonian theory was shown
to hold only as a limiting case of the special and general theories of
relativity, added a further twist to the question, for now all the
successes of Newtonian science, which still remain in place, have to be
seen as predicated on a theory that holds only to high approximation in
parochial circumstances.




The extraordinary character of the *Principia* gave rise
to a still continuing tendency to place great weight on everything
Newton said. This, however, was, and still is, easy to carry to
excess. One need look no further than Book 2 of the
*Principia* to see that Newton had no more claim to being
somehow in tune with nature and the truth than any number of his
contemporaries. Newton's manuscripts do reveal an exceptional
level of attention to detail of phrasing, from which we can rightly
conclude that his pronouncements, especially in print, were
*generally* backed by careful, self-critical reflection.
But this conclusion does not automatically extend to every statement he
ever made. We must constantly be mindful of the possibility of
too much weight being placed, then or now, on any pronouncement that
stands in relative isolation over his 60 year career; and, to counter
the tendency to excess, we should be even more vigilant than usual in
not losing sight of the context, circumstantial as well as historical
and textual, of both Newton's statements and the eighteenth century
reaction to
them.