1

Designing with Blends: Conceptual Foundations of Human-Computer Interaction and Software Engineering The MIT Press Manuel Imaz, David Benyon Year: 2007 Language: english File: PDF, 3.16 MB Your tags: 0 / 0

2

Elements of Photonics, For Fiber and Integrated Optics, Vol. 2 Wiley-Interscience Keigo Iizuka Year: 2002 Language: english File: PDF, 7.38 MB Your tags: 0 / 0

Newton: A Very Short Introduction

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Rob Iliffe

Newton
A Very Short Introduction

1

3

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Acknowledgements

I would like to thank Martin Beagles, John Young, Luciana
O’Flaherty, Larry Stewart, and Sarah Dry for commenting on earlier
versions of this work, and also for suggesting improvements.

This page intentionally left blank

Preface

In Victorian Britain, every schoolboy knew that Sir Isaac Newton
was an unrivalled mathematical and scientific genius, and most
would have been able to give a basic account of his central
discoveries. In optics, Newton found that white light was not a
fundamental element within nature but was composed of more
basic, primary rays being mixed together. Bodies appeared a
particular colour because they had a disposition to reflect or absorb
certain colours rather than others. In the realm of mathematics,
Newton discovered the binomial theorem for expanding the sum of
two variables raised to any given power, as well as the basic laws of
calculus. This treated the rate of change of any variable (the shape
of a curve or the velocity of a moving object) at any moment, and
also offered techniques for measuring areas and volumes under
curves (amongst other things). Both his mathematical and optical
work took many decades to be fully accepted by contemporaries, the
first because his work was shown only to a handful of
contemporaries, and the second because many found it hard to
reproduce and too revolutionary to be easily grasped.
The crowning glory of Newton’s system was contained in his
Principia Mathematica of 1687, in which he introduced the three
laws of motion and the incredible notion of Universal Gravitation –
the idea that all massive bodies continuously attracted all other
bodies according to a mathematical law. Using completely novel

concepts such as ‘mass’ and ‘attraction’, Newton announced in his
laws of motion (1) that all bodies continued in their state of motion
or rest unless affected by some external force; (2) that the change in
state of all bodies was proportional to the force that caused that
change and took place in the direction exerted by that force; and (3)
that to every action there was an equal and opposite reaction.
Investigating the consequences of his work in this area formed the
basis of celestial mechanics in the 18th century and made possible a
new and what we take to be correct physics (special and general
relativistic effects excepted) of the Earth and heavens. Not for
nothing was Newton held by the vast majority of educated people as
the Founder of Reason.
Apart from this, the elites of Victorian Britain grappled with more
difficult aspects of Newton’s life and work, for it was also known
that Sir Isaac was both a committed alchemist and a radical heretic.
Incontrovertible evidence also showed that he had behaved in a
reprehensible manner towards a number of his contemporaries.
Since then, explaining his personality and addressing the problem
of reconciling the ‘rational’ and ‘irrational’ aspects of his work have
continued to challenge historians. Moreover, the fact that many
important papers only became available for serious investigation in
the 1970s means that a well-balanced picture of his work has only
become possible in the last few decades.
Although it has long been known that he had these apparently
outlandish interests – which he undoubtedly understood to be more
significant than his more ‘respectable’ pursuits – recent popular
biographies of Newton have continually played up these less
orthodox elements as if they are being described for the first time.
Nevertheless, these books have neither offered new insights, nor do
they make use of the astonishing materials that have been made
available online in the last few years. Most of these works also make
overblown claims about the links between various spheres of
Newton’s intellectual activity. This introduction aims to redress
these problems by taking into account recent scholarly work as well

as the newly accessible online transcriptions of writings; as it
happens, the Newton that emerges is much stranger than has been
visible in recent accounts.

This page intentionally left blank

Contents

List of illustrations xv

1
2
3
4
5
6
7
8
9
10

A national man 1
Playing philosophically
The marvellous years

8
20

The censorious multitude 41
A true hermetic philosopher
One of God’s chosen few
The divine book

54

72

83

In the city 103
Lord and master of all

112

Centaurs and other animals 126
Further reading 133
Index 135

This page intentionally left blank

List of illustrations

1

Conduitt’s bust of
Newton, executed by
J. M. Rysbrack

8 The Philosopher’s
Stone
2

Courtesy of Dr Milo Keynes

2 The Source for Newton’s
water-powered clock 12
3 Cartesian vortices

57

© The Dibner Institute,
Cambridge, Mass.

9 The Whore of
Babylon

78

© The Trustees of the British
Museum

24

4 Perpetual motion
machines powered by
gravitational waves
31

10

The path of an object
dropped vertically
from a tall tower
84

5 Newton’s drawing of
his deformation
of his eye

11

Hooke’s hypothesis

85

12

Newton’s response

85

13

Flamsteed’s suggested
path for the comet of
winter 1680–1
87

40

By permission of
the Syndics of Cambridge
University Library

6 A sketch of Newton’s
telescope
7 The crucial
experiment

Leen Ritmeyer

44

Courtesy of the Royal Society

14
47

Courtesy of the Warden and
Fellows of New College, Oxford

Newton’s alternative
path for the comet

89

15

Newton’s proof
of Kepler’s Second
Law

17
91

Newton in 1726,
painted by Enoch
Seeman

131

Courtesy of Dr Milo Keynes

16

Newton’s proof that
an inverse-square law
governs elliptical
orbits
92

The publisher and the author apologise for any errors or omissions
in the above list. If contacted it will be pleased to rectify these at
the earliest opportunity.

Chapter 1
A national man

Unconscious since late on the previous Saturday evening, Sir Isaac
Newton died soon after 1 a.m. on Monday 20 March 1727 at the age
of 84. He was attended at his passing by his physician Richard
Mead, who later told the great French philosophe Voltaire that on
his deathbed Newton had confessed he was a virgin. Newton was
also looked after in his final hours by his half-niece Catherine and
her husband John Conduitt, who had acted as a sort of personal
assistant to Newton in his final years. Despite many demands on his
time, Conduitt almost single-handedly organized the
commemoration of the great man he had come to know, and he
heroically managed to supervise the collection of virtually all the
significant information that we have concerning Newton’s private
life. He was responsible for arranging Newton’s funeral at
Westminster Abbey at the end of March 1727, and he commissioned
Alexander Pope to compose the epitaph on Newton’s tomb. In the
following years he authorized the execution of numerous paintings
and busts of his hero by the greatest British and foreign artists of
the day.
Over a number of years Conduitt tried to write the definitive ‘Life’ of
Newton, although he never completed the task. He had recorded
details of some conversations he had had with Newton but for more
detail on Newton’s scientific work he asked a number of people to
send in their reminiscences. A week after Newton’s death he wrote
1

Newton

1. Conduitt’s own bust of Newton, executed by J. M. Rysbrack

to Bernard de Fontenelle, Permanent Secretary of the Paris
Académie Royale des Sciences, offering to supply the Frenchman
with material that he could use in his ‘Eloge’ of Newton. Conduitt
saw this as a chance to secure his relative’s reputation in the country
that had been most unwilling to recognize Newton’s pre-eminence
in science and mathematics. It would not be until the late 1730s
that Newton’s reputation was secure in France, and in the
immediate aftermath of his death Conduitt was keen that French
2

and other non-British scholars should be aware of Newton’s priority
in devising the calculus, an accolade most French scholars still
accorded to the German polymath Gottfried Leibniz. Over the
summer of 1727, Conduitt worked on a ‘Memoir’ of Newton, which
he sent off to Fontenelle in July.

Fontenelle’s ‘Eloge’ was read to the Académie in November 1727. He
gave a good account of Newton’s scientific and mathematical
development, accepting that virtually all of his great discoveries had
been made in his early twenties. He disagreed with many of the
tenets found in the Principia, especially that of the notion of
‘attraction’, but he was effusive about its overall significance.
Although he realized that Newton disagreed with many of the
theories of the great French mathematician and philosopher René
Descartes, Fontenelle noted that they had both attempted to base
science on mathematical foundations, and that both were geniuses
in their own time and manner. The Eloge was immediately
translated into English, becoming the dominant source for all
English-language biographies for over a century.
Other works appeared very quickly, one of which, William
Whiston’s Collection of Authentick Records, was the first text to
3

A national man

Conduitt’s ‘Memoir’ gave a factual if adulatory history of Newton’s
intellectual and moral life, and the latter was described as ‘pure &
unspotted in thought word & deed’. He was astonishingly humble,
exhibited great charitableness and such a sweetness and meekness
that he would often shed tears at a sad story. He loved liberty and
the Hanoverian regime of George I, ‘abhorred and detested’
persecution, and mercy to beast and Man was ‘the darling topick he
loved to dwell upon’. Conduitt included an account of Newton’s
early development at Cambridge, and added a one-sided version of
the priority dispute with Leibniz. Not only had Leibniz not been the
first to invent it but he ‘never understood it enough to apply it to the
system of the Universe which was the great & glorious use Sir Isaac
made of it’.

Newton

publicly challenge the view of Newton as a shining white knight.
Whiston was Newton’s successor as Lucasian Professor at
Cambridge but had been ejected from Cambridge in 1710 for
espousing heretical religious views similar to those held by Newton.
Revealing Newton’s radical theological views for the first time,
Whiston contrasted Newton’s ‘cautious Temper and Conduct’ with
his own ‘openness’, but remarked that Newton could not hide his
own momentous discoveries in theology, ‘notwithstanding his
prodigiously fearful, cautious, and suspicious Temper’.
Even before he read Whiston, Conduitt was peeved both at the
even-handed way with which Fontenelle had compared Newton
with Descartes and at his treatment of the priority dispute. He
immediately wrote again to a number of pro-Newtonians, pleading
in February 1728 that ‘As Sir I. Newton was a national man I think
every one ought to contribute to a work intended to do him justice.’
Of those letters he received in response, the most interesting were
two from Humphrey Newton (no relation), who as Newton’s
amanuensis (secretary) had a unique insight into Newton’s
behaviour during the years in which he had composed the Principia
(1684–7). According to Humphrey, Newton would sometimes take
‘a sudden stand, turn’d himself about, run up the Stairs, like another
Archimedes, with an eureka, fall to write on his Desk standing,
without giving himself the Leasure to draw a Chair to sit down in’.
Newton at this time apparently received only a select band of
scholars to his chambers, including John Francis Vigani, a chemistry
lecturer at Trinity. Vigani got on well with Newton until, according
to Catherine Conduitt, Vigari ‘told a loose story about a Nun’.
John Conduitt had already received crucial information from the
antiquarian William Stukeley, who had moved to Grantham shortly
before Newton’s death. Since this was where Newton had attended
the local grammar school while lodging with the local apothecary, it
was an ideal place to collect information relating to Newton’s youth.
By 1800 some of the Stukeley material but little from the Conduitt
papers had been published. In the early 19th century, however, new
4

information profoundly altered the way people thought of Newton.
In 1829 a translation of a recent biography of Newton by
Jean-Baptiste Biot revealed that he had suffered a breakdown in the
early 1690s. Still more damagingly, in the 1830s a barrage of
upsetting evidence emerged from the papers of the first Astronomer
Royal, John Flamsteed, which presented a tarnished view of
Newton’s demeanour. Thereafter, Victorians vied to offer accounts
of Newton’s life and works. Most importantly, David Brewster’s
Memoirs of the Life, Writings and Discoveries of Sir Isaac Newton
(1855), a greatly revised version of his Life of Sir Isaac Newton
(1831), became the dominant biography for over a century. He tried
valiantly to deal with Newton’s commitment to alchemy, his
unorthodox religious opinions, and his often graceless treatment of
both friend and foe, but was ultimately unwilling to recognize the
full extent to which Newton fell short of perfection.

The great economist John Maynard Keynes had attended part of
the Sotheby sale, and he set his energies towards acquiring all of
5

A national man

In the early 1870s the fifth Lord Portsmouth, a distant descendant of
Catherine Conduitt and owner of Newton’s papers, generously
decided to donate Newton’s ‘scientific’ manuscripts to the nation.
A committee was set up at Cambridge University to assess the
significance of the collection, and its results were reported in a
catalogue of the papers in 1888. The non-scientific papers,
including Newton’s alchemical and theological writings, were
generally deemed of little interest and they remained in the
Portsmouth family until they were sold off at Sotheby’s in 1936 for
the ridiculously small sum of just over £9,000. A syndicate
gradually acquired most of the theological papers from dealers, and
ultimately they were bought up by the collector Abraham Yahuda,
an expert in semitic philology. Yahuda died in 1951 and, although he
was an anti-Zionist, his astonishing collection of Newton’s papers
came into the possession of the Jewish National and University
Library in the Hebrew University of Jerusalem after a court case
lasting nearly a decade.

Newton’s alchemical papers, as well as all the ‘personal’ papers in
the hand of John Conduitt. By 1942, the tercentenary of Newton’s
birth, Keynes was in possession of the vast majority of Newton’s
alchemical papers, along with some theological tracts. Although he
was preoccupied by the demands of the Second World War, Keynes
gave a talk based on these materials as part of the muted
tercentenary celebrations. His Newton was far more extraordinary
than the person presented by previous biographers, being a ‘Judaic
monotheist of the School of Maimonides’, neither a ‘rationalist’ nor
‘the first and greatest of the modern age of scientists’, but
the last of the magicians, the last of the Babylonians and Sumerians,
the last great mind which looked out on the visible and intellectual
world with the same eyes as those who began to build our

Newton

intellectual inheritance rather less than 10,000 years ago.

Newton saw the twin worlds of nature and obscure texts as one
giant riddle that could be unravelled by decoding ‘certain mystic
clues which God had lain about the world to allow a sort of
philosopher’s treasure hunt to the esoteric brotherhood’. His
writings on alchemical and theological topics were, Keynes argued,
‘marked by careful learning, accurate method, and extreme sobriety
of statement’ and were ‘just as sane as the Principia’.
The two most influential scholarly biographies of the late 20th
century both made extensive use of manuscript materials. Frank
Manuel’s A Portrait of Isaac Newton of 1968 offers a
psychoanalytical account of Newton’s personality that is heavily
reliant upon the assumption that Newton’s unconscious behaviour
expressed itself ‘primarily in situations of love and hate’. According
to Manuel, the source of Newton’s psychic problems lay in the fact
that she remarried when Newton was only 3 years old. Having
already lost his biological father, who died only months before he
was born, Newton became hostile to his stepfather and devoted
himself to the one Father he could really recognize – God. Manuel
showed how the traumatic experiences of Newton’s youth were
6

internalized, and the brilliant but tormented young Puritan became
the ageing despot of the early 18th century.
In his more orthodox Never at Rest: A Scientific Biography of Isaac
Newton of 1980, Richard S. Westfall took Newton’s work as the
central aspect of his life. Drawing from the full range of Newton’s
manuscripts that were now available to scholars, his ‘scientific
biography’ engaged with every aspect of Newton’s intellectual
interests, although his scientific career ‘furnishes the central theme’.
While he deals ably with Newton’s intellectual accomplishments, it
is apparent that Westfall’s great admiration for this part of
Newton’s life does not extend to his personal conduct.
Ultimately Westfall came to loathe the man whose works he had
studied for over 2 decades. He was not the first to feel this way
about the Great Man.
A national man

7

Chapter 2
Playing philosophically

According to the calendar then in use in England, Newton was born
on Christmas Day 1642 (4 January 1643 in most of Continental
Europe). The first decade of his life witnessed the horror of the civil
wars between parliamentary and royalist forces in the 1640s,
culminating in the beheading of Charles I in January 1649. His
uncle and stepfather were rectors of local parishes, and they seem to
have existed without much harassment from the church authorities
convened by Parliament to check for religious ‘abuses’. In his second
decade he lived under the radical Protestant Commonwealth, which
was replaced in 1660 when Charles II was restored to the throne.
Newton was born into a relatively prosperous family and was
brought up in a devout atmosphere. His father, also Isaac, was a
yeoman farmer who in December 1639 inherited both land and a
handsome manor in the Lincolnshire parish of Woolsthorpe. His
mother, Hannah Ayscough, came from the lower gentry and (as was
common for the period) seems to have been educated at only a
rudimentary level. Nevertheless, her brother William had
graduated from Trinity College Cambridge in the 1630s and would
be influential in directing Newton to the same institution.
Newton’s father, apparently unable to sign his name, died in early
October 1642, almost three months before the birth of his son.
Newton told Conduitt that he had been a tiny and sick baby,
thought to be unlikely to survive; two women sent to get help from a
8

Newton went to two local schools until he was 12, after which he
went to Grantham Grammar School. Here he lodged with a local
apothecary, Joseph Clark, whose shop proved to be a great source of
information. A descendant of Clark told William Stukeley that
Newton showed an immense interest in the abundant medicines
and chemicals, and Stukeley noted that he spent a great deal of time
gathering herbs, probably learning about their properties from
Clark’s apprentices. Newton lived with Clark’s stepchildren, one of
whom, Catherine, who grew up to be a Mrs Vincent, provided
abundant information about the prodigy. Everyone Stukeley met
recounted ‘the extraordinary pregnancy of his genius’ for building
machines and told him ‘that instead of playing among the other
boys, when from school, he always busyed himself at home, in
making knickknacks of divers sorts, & models in wood, of whatever
his fancy led him to’. Mrs Vincent, allegedly the object of amorous
attention from the young inventor, recorded that his schoolfellows
were ‘not very affectionate’ towards him, aware ‘that he had more
9

Playing philosophically

local gentlewoman stopped to sit down on the way there, as they
were certain the baby would be dead on their return. Surviving
against the odds, Newton was brought up by his mother until the
age of 3, when she was approached with an offer of marriage by
Barnabas Smith, an ageing vicar of a local parish. Smith was
wealthy, and they married in January 1646 after he had promised to
leave some land to her first born. Spending most of her time with
her new spouse, she produced three more children before his death
in 1653 (one of whom would be the mother of Catherine Conduitt).
Although John Conduitt waxed lyrical about Hannah’s general
virtues, and was careful to point out that she was ‘an indulgent
parent’ to all the children, he emphasized that young Isaac was her
favourite. Whatever the truth of this, Newton’s own evidence
indicates that, as a teenager, he had an extremely difficult
relationship with his mother, and historians have always found it
difficult to make Conduitt’s account tally with the fact that for seven
years Newton was effectively left in Woolsthorpe to be brought up
by his maternal grandmother.

Newton

ingenuity’ than they did. Instead, little Isaac was ‘always, a sober,
silent, thinking lad’, who never played with boys but who would
occasionally make dolls house furniture for the girls ‘to set their
babys, and trinkets on’.
Newton built up ‘a whole shop of tools’ in Grantham, spending all
the money his mother gave him on saws, chisels, hatchets, hammers
and the like, ‘which he would use with as much dexterity, as if he
had been brought up to the trade’. Many of the machines described
by Mrs Vincent and others had been originally set out in a book by
John Bate entitled Mysteries of Nature and Art, part of an extremely
popular genre of ‘mathematical magic’ books that contained
numerous recipes and drawings of machines. Newton was already
unwilling simply to appropriate information without developing it
in a dramatic fashion. Not content with reproducing a simple
windmill described in Bate, he went to see a real version being
constructed in a neighbouring village, ‘was daily with the workmen’
and ‘obtain’d so exact a notion of the mechanism of it, that he made
a true, & perfect model of it’. He went beyond his prototype and
adjusted the mechanism so that the sails were powered by a mouse,
which drove a wheel in its efforts to reach some corn. While
Stukeley’s informants disagreed as to its exact mechanism, they
concurred that people would come from miles around to see Isaac’s
‘mouse miller’. Stukeley perceptively noted that ‘ludicrous’ (i.e.
playful) devices commonly grabbed his attention. Apart from the
mouse miller and the dolls’ furniture, Newton examined the fabric
and dimensions of a simple kite, built a better example, and
attached a candle-lit lantern to it, frightening the countryfolk and
giving them much to discuss as they drank their beer.
As in the cases of the windmill and the kite, Newton made a wooden
clock and then immediately built a better one. This improved
version, which had a dial, was powered by a steady trickle of water
that he supplied each morning, and was made from a box given to
him by Humphrey Babington. Babington, the brother of Mrs Clark
(a close friend of Hannah Smith), had been ejected from Trinity
10

College for refusing to take the engagement oath of allegiance to the
Commonwealth, and would play a significant role in Newton’s life
over the following decades. Extending his virtuosity still further,
Newton graduated to complex sundials, turning various features of
Clark’s house into different sorts of clock and, according to Stukeley,
‘showing the greatness, & extent of his thought by drawing long
lines, tying long strings with running balls upon them; driving pegs
into the walls, to mark hours, half hours & quarters’. He made an
‘almanac’ of these lines, ‘knowing the day of the month by them; the
suns entry into signs, the equinoxes, & solstices’. ‘Isaac’s dials’, like
many of his other accomplishments, became well known in the
parish. Perhaps the greatest of his juvenile achievements, Stukeley
believed that these were the origins of his fascination for heavenly
motions.

Newton’s artistic bent at this time can be gauged by a series of notes
on Bate’s book, entered into a notebook that he purchased in 1659.
These notes attest to Newton’s concern with the practical aspects of
drawing, and also his interest in producing a wide variety of
coloured inks and paints, whether from animals, vegetables, and
minerals, or by mixing pre-existing colours. Just over a decade later,
the last of these topics would make him famous. Other instructions
concerned how to make fishbait and different ways, not all of them
overly complicated, of catching birds by making them drunk. Bate’s
book also contained recipes for universal salves and ointments, a
number of which Newton noted down. Indeed, one of the few things
later recalled by John Wickins, his roommate of 20 years at
Cambridge, was that Newton would often take a grisly self-prepared
11

Playing philosophically

Newton also excelled in artistic pursuits, such as drawing and even
the composing of poetry, though his penchant for verse would prove
temporary. He covered the walls of his attic room with charcoal
drawings of animals, men, plants and mathematical figures, and
scratched his name into the shelves. In the middle of the 20th
century, geometrical drawings, undoubtedly by Newton, were
discovered etched onto the stonework of Woolsthorpe Manor.

Newton

2. The source for Newton’s design for a water-powered clock, from
John Bate’s Mysteries of Nature and Art

concoction (‘Lucatello’s balsam’) as a preservative. Some notes came
from John Wilkins’s Mathematical Magick, a popular work that
purveyed similar information to Bate, while other entries in the
notebook concerned different ways to produce perpetual motion, a
topic of extreme interest in the following decades.
This immersion in worlds of practical ingenuity not only offered
portents of his great future, but led directly to it. Indeed, Stukeley
gave a superb account of how Newton’s early obsessions related to
his later triumphs. He pointed out that Newton’s early mastery at
using mechanical tools, along with his expertise in drawing and
designing, was extremely useful for his experimental skill and
‘prepar’d for him a solid foundation to exercise his strong reasoning
12

facultys upon’. Uniquely Newton had all the qualities for becoming
a great natural philosopher, such as ‘profound judgement’,
‘invincible constancy, & perseverance in finding out his solutions’, ‘a
vast strength of mind, in protracting his reasonings [and] his chain
of deductions’, and an ‘incomparable skill in algebraic, & the like
methods of notation’. Like all children he was an imitator, but for
Stukeley ‘he was in reality born a philosopher. Learning, & accident,
& industry pointed out to his discerning eye some few, simple &
universal truths’, which he gradually extended ‘till he unfolded the
œconomy of the macrocosm’.

A godly child

Some episodes were those common to any teenager in his village.
13

Playing philosophically

Absorbed as he was in making his devices, the gifted country boy
was a deeply unhappy youth. Late in May 1662 he recorded a list in
shorthand of all the sins he had committed in the previous decade,
and for a short time he noted down all the misdemeanours
committed while at Cambridge. The term ‘Puritan’ is strictly false as
a description of Newton’s religious doctrine but the radical
Protestant ethical values associated with this term accurately
describe the person who appears in the entries. Many of the sins
cover activities performed on the Sabbath (‘Thy day’), when godly
Christians were supposed to rest. On various Sundays in the 1650s,
Newton read a frivolous book, ate an apple in chapel, and made a
feather, a clock, a mousetrap, some rope, and in the evening some
pies. He confessed to ‘idle discourse’ on God’s day, so that it is not
surprising that he also carelessly heard and committed to memory
various sermons, while he also recorded that he completely missed
chapel on one occasion. Sometimes he had set his heart on learning
and money more than on God, preferring ‘worldly things’ instead,
and indeed many of the sins recall his failure to live as a godly man.
‘Not living according to my belief’ and ‘neglecting to pray’, he had
become distant from God, failing to love God for Himself and
failing to ‘long’ for God’s ordinances.

Newton

He put a pin in another boy’s hat to ‘prick’ him, refused to come
home when his mother told him to, and lied to his mother and
grandmother about having a crossbow. At other times, he ‘fell out’
with servants. Food crimes were also prominent: he stole cherry
cobs from Edward Storer, Clark’s stepson, and pilfered plums and
sugar from his mother’s foodbox. He even confessed to gluttony
while he was ill, and indeed the first entries in the short list of sins
committed when he was a student at Cambridge were for the same
offence. Other comments in the first list portray darker elements of
his psyche. He punched one of his sisters, struck ‘many’, and beat up
Arthur Storer, Edward’s brother. The precise meaning of ‘Having
unclean thoughts words and actions and dreams’ in Newton’s list is
unclear, as is his lament that he had used ‘unlawful means’ to bring
himself out of ‘distress’. Real loathing shows through his
recollection of ‘wishing death and hoping it to some’, and most
horrifying of all is the distant memory of having threatened to burn
his stepfather and mother along with their house. Newton also
compiled a list of common words arranged alphabetically in Francis
Gregory’s Nomenclatura brevis reformata of 1651. To terms like
‘Father’, ‘Wife’, and ‘Widdow’, Newton added words such as
‘Fornicator’ and ‘Whoore’ not found in Gregory, expressions that
perhaps refer to his view of his mother and stepfather.
Newton’s anger manifested itself in other areas of his life. According
to Conduitt, who knew him well, resentment and the desire to
emulate had been the forces propelling Newton to outdo all others
at the start of his academic career. Newton often told him a story
about his early days at the grammar school when he was at the
bottom of the class, a narrative that is possibly connected with his
‘confession’ about beating Arthur Storer. One day he was kicked in
the stomach on his way to school. After lessons had ended he fought
in the churchyard with his assailant, and although Newton ‘was
not so lusty as his antagonist he had so much more spirit &
resolution that he beat him till he declared he would fight no
more’. Later, the schoolmaster’s son goaded him into forcing his
antagonist’s face into the side of the church. After this, Newton
14

strove to outdo his opponent in learning, not stopping until he
had risen above him in the pecking order. Inexorably, he rose to
become top of the school.

It is at this point that narratives of Newton’s development begin to
portray him as an unworldly scholar rather than as a gifted
mechanic. Later, a number of different pieces of evidence indicate
that he became famous for his unworldly or ‘insensate’ behaviour
when he went to Cambridge. A hopeless manager of his family’s
affairs, he would bribe the servant to act on his behalf, and he would
find scholarly refuge in the attic where he had lodged while at the
school, engrossed in a pile of medical and scientific tomes that had
been left there. On other occasions, he would simply lie under a
hedge or a tree and read a book. Once Newton’s horse slipped his
bridle, and he walked on unawares for miles, engrossed in a book he
was reading. His mother was ‘not a little offended at his
bookishness’, while the servants called him ‘a silly boy’ who ‘would
never be good for any thing’.
15

Playing philosophically

His extracurricular activities had an adverse effect on his schooling
but such was his ability that he could resume his academic work and
outperform his schoolfellows whenever he wanted. Stukeley noted
that ‘dull boys were sometimes put over him, in form, but this
always excited him to redouble his pains, to overtake them’. The
headmaster of the school, John Stokes, seems to have spotted
Newton’s talent at an early stage, but could not coax the lad away
from his hammers and chisels. However, in the latter half of 1659
his mother decided to pull him out of school to run the family
estate. Despite being put in the care of a trusty servant, his
obsession with building waterwheels and other models and a
capacity to be lost in his books made Newton completely unsuitable
for the task. The sheep and cows he was supposed to be looking
after strayed into neighbouring fields, and records show that he
was fined for this in October of the same year. He could barely
remember to eat and, according to Stukeley, ‘philosophy absorbed
all his thoughts’.

To the rescue came Stokes, who told Hannah that Newton’s
immense talent should not be buried in ‘rustic business’. He saw ‘the
uncommon capacity of the lad, & admired his surprising inventions,
the dexterity of his hand, as well as his wonderful penetration, far
beyond his years’, telling his mother that he ‘would become a very
extraordinary man’. Stokes offered to let him board for free,
possibly a key factor in Hannah allowing her son to go back to the
grammar school to prepare for university. Returning there in the
autumn of 1660, he received extra tuition in Latin and Greek, and
on his final day was given a rousing send-off by Stokes, allegedly
driving the rest of the school to tears. Stukeley noted that no such
sentiment was felt by the servants, who declared him ‘fit for nothing
but the Versity’.

Newton

Trinity
By this time it had already been decided that he would go to Trinity
College Cambridge, the most prestigious college in England. The
combined forces of William Ayscough and Humphrey Babington,
newly restored as a fellow, were probably decisive in sending
Newton there. Newton arrived in Cambridge on 5 June 1661 in the
relatively menial position of ‘subsizar’, a lowly status strangely out
of keeping with the wealth that his mother commanded. Subsizars,
who had to pay for their own food and also to attend lectures, were
effectively servants of fellows or wealthy students, and it is possible
that Newton worked in this position, however notionally, for
Babington. Both town and gown had reacted quickly and positively
to the restoration of Charles II the previous spring, and in the most
senior positions royalist sympathizers had replaced Commonwealth
appointees. The Anglican scholar John Pearson, author of the
highly influential Exposition of the Creed in 1659, became master in
1662, and under him the college emphasized more traditional forms
of scholarship and in particular theological study.
Evidence from a small notebook sheds some light on how Newton
spent his time and money as an undergraduate. Early entries show
16

his purchase of basic equipment such as books, paper, pen and ink,
and the ordinary materials for living in 17th-century student
accommodation, such as clothes, shoes, candles, a lock for his desk,
a carpet for his room, and a chamberpot. He bought a watch, a
chessboard and later a set of chess pieces (according to Catherine
Conduitt, he became extremely proficient at board games), and paid
seven pence as his yearly subscription for access to the tennis court.
The entry ‘to balls & barges’, repeated later on, indicates that not
every moment was spent in study in his first year there. Indeed, he
created a separate list of ‘frivolous’ and ‘wasteful’ expenses,
including the purchase of cherries, beer, marmalade, custard tarts,
cake, milk, butter, and cheese. Later, he graduated to apples, pears,
and stewed prunes.

17

Playing philosophically

Very quickly – and uniquely among undergraduates for whom
records survive – Newton began to lend money to his bedmaker
and to fellow students, many of them ‘pensioners’ who occupied a
social rank in the college somewhat higher than his. Most
recipients of Newton’s generosity paid him back, as indicated by a
cross through the relevant record. At some point, probably in 1663,
Newton met another pensioner, John Wickins (whose son Nicholas
recorded that his father had found Newton ‘solitary and dejected’),
and they decided to room together. Wickins would occasionally act
as an amanuensis for Newton until he left Cambridge in 1683 to
take up a position in the church. Nick Wickins was told by his
father that Newton would forget his food when working and in
the morning would arise ‘in a pleasant manner with the
satisfaction of having found out some Proposition; without any
concern for, or seeming want of his Nights sleep’. If Newton’s
recollections are correct, in the same year he met Wickins, he
became fascinated by judicial astrology – the assessment of an
individual’s future prospects on the basis of studying the positions
of the stars and planets – and bought a book on the topic. It was as a
result of being dissatisfied with this that he turned the following
year to the mathematics of Euclid, only to reject it as trivially
obvious.

Newton

He probably attended the initial Lucasian mathematical lectures of
Isaac Barrow, the first holder of the chair, in March 1664 – and the
professor may have noted a particularly attentive student in the
audience. In the month after Barrow’s inaugural lecture, Trinity
held one of its periodic scholarship competitions, which Newton
entered. As he told the story later, Barrow was his examiner and –
never imagining that the young student had ventured into
Descartes’s formidable Géometrie, a feat that Newton was
apparently too modest to admit – was dismayed by Newton’s lack of
knowledge of Euclid. Newton got the scholarship nevertheless, and
thus became entitled to a number of privileges. Early the following
year, at about the same time as he discovered the generalized
binomial theorem, he was forced to undertake a protracted
examination in more standard learning to qualify for his Bachelor
of Arts degree. A later tradition held that he almost failed this exam,
although the story may be a confusion of this event with the
scholarship examination of the previous year.
Plague devastated various parts of England in the middle of 1665
and, along with most other students, Newton returned home some
time in late July or early August. Having come back to Cambridge in
March 1666, he continued to lend money to many of the same
students as before, but when a resurgence of the plague occurred in
early summer, he again sought refuge in Lincolnshire. Much of his
most innovative work was produced here, probably at the home of
Babington in Boothby Pagnell. On 20 March 1667 he received £10
from his mother, who gave him the same amount when he returned
to Cambridge in the following month. Over the next year, he spent
much of this money, as well as funds repaid by debtors, on
equipment for grinding tools and performing experiments, three
pairs of shoes, losing at cards (twice), drinking at a tavern (twice),
some early volumes of the Philosophical Transactions, Thomas
Sprat’s recently published History of the Royal Society, and some
oranges for his sister. In September he entered another
competition, this time for a college fellowship. Whether because of
support from Babington or Barrow, or simply because his brilliance
18

and dedication to scholarship shone through during the four days of
the oral examination, Newton was elected minor fellow.

19

Playing philosophically

Evidently, this also implied that he was expert in the sort of
theological scholarship demanded by Pearson and, as a
consequence of his election, he swore to make theology the focus of
his studies and to take holy orders – or resign. Soon afterwards he
moved to a new room, and revamped it to suit his tastes. In July
1668 he was made a Master of Arts, allowing him to progress to the
position of major fellow of the college. He spent more money on
material for his gown, and purchased an expensive hat, a suit, some
leather carpets, a couch (jointly bought with Wickins), and some
materials for a new featherbed. He also bought three prisms at one
shilling each, along with ‘glasses’, presumably for chemical
experiments, while in late summer he made his first trip to London.
His reputation would soon follow him.

Chapter 3
The marvellous years

The first decades of the 17th century witnessed an exponential
growth in the understanding of the Earth and heavens, a process
usually referred to as the Scientific Revolution. The older reliance
on the philosophy of Aristotle was fast waning in universities,
although across Europe Aristotelian natural philosophy and ethics
would be routinely taught at undergraduate level until the end of
the century. In the Aristotelian system of natural philosophy, the
movements of bodies were explained ‘causally’ in terms of the
amount of the four elements (earth, water, air, fire) that they
possessed, and objects moved up or down to their ‘natural’ place
depending on the preponderance of given elements of which they
were composed. Natural philosophy was routinely contrasted with
mathematics or ‘mixed mathematical’ subjects such as optics,
hydrostatics, and harmonics, where numbers could be applied to
measurable external quantities such as length or duration. All this
took place in a cosmos where the Earth was planted at the centre,
surrounded by the Sun and the planets.
The first dramatic change took place in astronomy, where despite
official opposition from the Catholic Church and from many
Protestant denominations, the Copernican heliocentric
(sun-centred) system gained new converts. Between 1596 and 1610,
there was an astronomical revolution galvanized by the work of
Johannes Kepler and Galileo Galilei. Kepler’s Mysterium
20

Cosmgraphicum of 1596 posited a heliocentric system in which the
distances between the planets could be determined by inscribing
the orbits of the planets inside regular solids. He published a
magnetic theory of planetary motion in his great Astronomia Nova
of 1609, a treatise that contained the first two of what were later
known as Kepler’s Laws (that planets move in ellipses, and that
with respect to the Sun, located at one of the foci of a particular
orbit, all planets swept out equal areas in equal times).

Galileo’s contribution to 17th-century science did not end with his
work in astronomy. In 1632 he bravely published his Dialogo sopra i
due Massimi Sistemi, a work which attempted to prove the
Copernican system of the world. For this he was placed under house
arrest until the end of his life in 1642, although his brilliant Discorsi
e Demonstrazioni Matematiche Intorno a Due Nuove Scienze
appeared in 1638. Aristotle had assumed that projected bodies first
experienced ‘violent’ motion, which was then taken over by the
‘natural’ motion that drove the earthy particles of the object
downwards to their natural place. He had also argued that bodies
21

The marvellous years

In 1609 Galileo developed a combination of lenses into a device that
allowed him to magnify objects. He turned this ‘telescope’ to the
heavens and realized that Jupiter had a series of satellites that
orbited it, just as the planets orbited the Sun. In his short Sidereus
Nuncius of 1610, he also announced that the Moon had mountains
and valleys, and that the Milky Way was composed of thousands of
stars. In 1613 he would further challenge the standard view, which
held that the heavens were ‘incorruptible’, by demonstrating that
the Sun had spots. Kepler would add his Third Law in his
Harmonice Mundi in 1619, which stated that for any planetary
orbit, the ratio between the cube of the mean radius of the planet
from the Sun, and the square of its period of revolution, was
constant. While Galileo’s discoveries effectively demolished belief in
the perfection of the heavens, Kepler’s laws would be of central
importance for Newton in demonstrating key propositions in the
Principia.

Newton

fell at speeds proportional to their weight. Instead, Galileo
announced in the Discorsi that the trajectory of projectiles was
parabolic, while the vertical component of a body near the surface
of the Earth could be expressed as a law according to which – for
bodies of any weight, or ‘bulk’ – the total distance fallen vertically is
proportional to the square of the time taken. He also made it clear,
again in opposition to the entire Aristotelian project, that the
physical causes of gravity were unimportant, and indeed, would be
extremely difficult to uncover. In showing that a number of
phenomena in the terrestrial sphere were mathematizable, Galileo
laid the basis for the modern science of mechanics. Newton’s great
triumph – expressed in his momentous work of the same name –
was to show that ‘mathematical principles’ were at the basis of many
more natural phenomena.
Another essential dimension of modern science was outlined in the
work of Francis Bacon. At the same time that Galileo and Kepler
were developing astronomy and mechanics, Bacon was promoting
the idea that the proper way to understand nature was to directly
engage with it rather than approach it through the medium of
Aristotelian (or any other) texts. Arguing that a collaborative
project was the only way to achieve progress in natural philosophy,
Bacon pointed to the recent discoveries of America and the Pacific
Ocean and praised the advances made by arts and trades.
Observations of disparate facts would increase knowledge of the
visible world while well-designed experiments would break the
natural world down into its constituent parts and convey
information about nature’s real secrets. Bacon even praised the way
in which alchemists were prepared to analyse nature, though he
lamented their closeted lifestyles and opaque jargon.
Not all anti-Aristotelians agreed that Galileo’s project was the
proper way to uncover scientific truths. René Descartes developed a
sophisticated account of the sorts of nano-structures underlying the
physical world. He assumed that the machine-like phenomena that
existed in the world around us also operated at the invisible level. In
22

his mechanical philosophy, an unseen microworld was populated
with hooks and screws, which made elements cohere. Large-scale
phenomena such as magnetism, heat, gravity, and electricity were
explained through the activity of a giant solar ‘vortex’, which by
spewing out various sorts of matter had major effects on terrestrial
phenomena. Descartes shared Galileo’s anti-Aristotelianism
(and secretly, his and Kepler’s Copernicanism) but he accused
the Italian of ‘building without foundation’, arguing that
scientific explanations needed to be couched in terms of the
micro-mechanical building-blocks of nature. This, as we shall see,
was the most influential work for the young Newton, although it
was soon the object of his critical animus.

A mathematical tyro

Towards the end of 1664 Newton found out how to measure the
‘crookedness’ or slope of a curve at any point. This was known as the
23

The marvellous years

At first, Newton’s education, was that of a standard Cambridge
undergraduate, and he was required to read a substantial amount of
the prescribed theological and Aristotelian literature. It may well
have been the Lucasian lectures of Barrow in the spring of 1664 that
spurred his interest in serious mathematics, and Newton later
recorded that he read William Oughtred’s Clavis Mathematicae and
Descartes’s Géometrie about the time that Barrow began lecturing.
In the winter of 1664–5 he closely studied the analytic mathematics
of Descartes (and the commentary in his edition of the latter’s
Géometrie by the Dutch mathematician Frans Van Schooten),
François Viète’s work on algebra, and John Wallis’s ‘method of
indivisibles’. Using what we call Cartesian co-ordinate geometry,
he mastered the equations that defined the various conic sections
(circles, parabolas, ellipses, and hyperbolas). Although he had
initially underestimated the achievement of Euclid in his Elements,
he would later revere the classical accomplishments of Euclid and
Apollonius, taking their approach to be the template for doing
mathematical work.

3. Cartesian vortices: the solar system, surrounding the Sun, S, being
bounded by FFFFGG. Other systems have stars at their centre.

‘problem of tangents’, and was being developed by mathematicians
such as James Gregory and René François de Sluse. Newton soon
built on an approach formulated by Descartes, by which the
‘normal’ to a curve (i.e. the line perpendicular to the tangents) could
be determined by finding the radius of curvature of a single large
circle at the point at which it touches the curve. Newton took the
‘normals’ between two close points, allowing the distance between
them to become arbitrarily small. He could now find the tangent to
any point on equations that ‘expressed’ any conic section, as well
as the maxima and minima of related equations. He generalized
the procedure to express the basic elements of what we call
differentiation, by which the slope of the tangent represents the rate
of change of a curve at any point.

Newton read Wallis carefully in the winter of 1664–5 and offered
alternative techniques for achieving the same results. Soon he
refined Wallis’s technique so as to consider the quadratures of
curves with fractional powers (i.e. involving square, cube, and other
roots). He went beyond Wallis by finding the correct series to square
the circle and as a result of extending the insights gained from this
success, he eventually discovered the generalized binomial theorem
(i.e. for fractional as well as integral powers) for expanding any
25

The marvellous years

As early as the winter of 1663–4 he had begun to read Wallis’s
analysis of the ways in which areas under sections of a curve could
be found by dividing the space into infinitely small sections. By the
time Wallis published his Arithmetica Infinitorum in 1655, it was
known that for basic equations x = yn , the area under the curve
between 0 and a was an + 1/n + 1. This was known as ‘squaring’ or
‘quadratures’, and was the embryonic form of what we now call
integration. More complex equations demanded different
techniques such as the use of infinite series, which allowed an
approximation to a final value as a series of terms reached a limit.
Wallis had developed this idea, squaring the parabola and
hyperbola and discovering a series of terms that approached the
value of π.

Newton

equation of the form (a + x)n/m, publicly announced for the first
time in a letter to Leibniz in 1676.
Early in 1665 Newton understood generally that the techniques of
tangents and of quadratures were inverse operations, that is, he had
the fundamental theorem of the calculus. By late 1665, and possibly
in imitation of Barrow, he was routinely treating curves as points
that carved out lines in a virtual space under certain conditions, and
he referred to the ‘velocities’ that points experienced in given
moments of time. This was what he called the ‘fluxional’ calculus,
because the values of points on the curve ‘flowed’ from one point to
the next. Areas under curves could now be treated not just as sums
of infinitely small segments, but as areas ‘kinematically’ created by
considering the space traversed by lines connecting a moving point
to corresponding values directly beneath the point on the x-axis.
Most of this brilliant work was systematized in an extraordinary
essay of October 1666, a treatise that marked him out as the leading
mathematician in the world.

The apple
The story that Newton was prompted by a falling apple to think of
comparing the force that caused the apple to fall with that required
to keep the Moon in its orbit is arguably the best known tale in the
history of science. Whether or not it is true, at the same time as he
made his mathematical discoveries he was branching out into an
extraordinary series of researches into mechanics that would make
him the first to unite the forces governing motions on earth and in
the heavens. By his own admission, Newton began his novel
insights by discovering the law by which a revolving body was kept
in its orbit. He soon wrote out a series of laws of motion, many of
which he would recall (and develop) when he wrote the Principia
20 years later. In a notebook entitled the ‘Waste Book’, in early
1665 he wrote out over a hundred axioms of motion. These
embraced the basic notion of inertia while he also invoked a
metaphysical justification for holding that the effects of impacts had
26

to be equal to their cause, an embryonic version of what would be
the third Law of Motion in his Principia. Taking into account the
bulk of a body and its velocity, Newton’s exquisite analysis led to a
law stating the conservation of momentum (mv) before and after
impact.

Newton now realized that he could attack a problem first raised by
Galileo, namely the ratio between the force that keeps an object on
Earth (gravity) with the ‘centrifugal force’, the tendency of the same
body to be flung off into space by the Earth’s rotation. For the first
he independently derived g, the acceleration due to gravity. For the
second he determined that centrifugal force would propel a body in
one revolution of the Earth through the length 2π2r, and with a
value for the size of the Earth he concluded that the force of gravity
was about 350 times stronger than centrifugal force (in one second
gravity would make a body descend 16 feet, while centrifugal force
would make it travel just over half an inch).
27

The marvellous years

Next, Newton adroitly investigated the path of a body being
bounced from the sides of an enclosed square, imagining that the
sum total of the four impacts exerted by each side of the square
was analogous and equal to the total force that would be required
to keep a body in orbit around a central point. On the assumption
that the number of sides exerting an impact could be made
infinitely large (so that it was a circle), he concluded that the total
force required to keep the body moving in a circle in one
revolution was ‘to the force of the bodies motion as all those sides
[i.e. the circumference of the circle] to the radius’. If the ‘force of
the bodies motion’ was mv, then the total force exerted in one
revolution was 2πmv. If the time taken for one revolution was
2πr/v, then the force divided by the time, expressing the force
acting on a revolving body at a given instant, was mv2/r. This
seminal result in the development of mechanics was first
published by Christiaan Huygens in 1673, although years before
this Newton had already used it to go beyond what Huygens
would achieve.

Newton

Perhaps influenced by seeing the fall of the apple, in the late 1660s
Newton compared the tendency of the Moon to leave the Earth with
the force of gravity at the Earth’s surface, a problem suggested by
Galileo. By using a figure for the size of the Earth that made the
Moon about 60 Earth radii (i.e. the distance from the centre of the
Earth to the equator) distant, he deduced that the tendency of an
object to recede from the Earth’s equator (its centrifugal force) was
about 12 and a half times that of the Moon to recede from the Earth.
If the regularity of the Moon’s orbit required the centrifugal force to
balance the centrally directed attraction exerted by the Earth, then
the centrifugal force of the Moon was equal to 350 × 12.5 (= 4325)
times the gravitational pull of the Earth at its surface.
In the same manuscript in which he made this calculation, Newton
derived the inverse-square (1/r2 ) distance law for the force exerted
on a revolving body by inserting his own law for the force of a
revolving body into Kepler’s Third Law. Newton would later recall
that his figure for the force keeping the Moon in its orbit (i.e. 4325)
‘answered pretty nearly’ to that produced by taking into account the
square of the distance between the Moon and the Earth (602
= 3600) demanded by the inverse-square law. At this point he
attributed the difference between these results to the effects of a
terrestrial vortex; later he would realize that it was due to an
incorrect measurement for the size of the Earth. He would also
come to see this incredible effort as evidence for his priority in
devising Universal Gravitation. However, amazing as it was, it
lacked many of the elements of his great theory.

Philosophical questions
These interests by no means exhausted Newton’s scientific fertility,
and in another notebook he took a series of notes from Aristotelian
texts and from commentaries on them. These covered subjects in
the general curriculum that would be studied by any student in a
European university, such as ethics, logic, rhetoric, and natural
philosophy. At some point, probably late in 1664, he stopped taking
28

excerpts from the Aristotelian textbooks and entered a series of
notes and philosophical queries under the heading ‘Certain
Philosophical Questions’. Above the title he noted a common phrase
that in English reads ‘Plato is my friend, Aristotle is my friend, but
truth is a greater friend’.

Newton would remain committed to a Cartesian-style vortex until
the early 1680s. The finest parts of the vortex he termed the
‘ethereall mater’, although later he would use the word ‘aether’ to
distinguish this pervasive but undetectable medium from the
coarser ‘air’. He queried whether the agitation of the vortex caused
objects to heat up, and also wondered whether heat was caused by
air moved by light, or directly by light itself. He also posed the
question of whether water could be made to freeze by removing its
heat inside Boyle’s air-pump (which evacuated or compressed air
inside a glass chamber). As for the downward motion of the
29

The marvellous years

The initial entries in the ‘Philosophical Questions’ notebook were
composed under headings concerning the nature of matter, the
reason why some tiny bodies ‘cohered’ together to form larger
bodies, the nature of heat and cold, and the question of why some
bodies fell and some rose. He made compelling criticisms of
conventional views, and indeed the general topics on which he
commented would be the focus of his interest for the rest of his life.
The earliest entries have a metaphysical flavour to them, which is
very different from the more experimental approach he would soon
adopt. Regarding the nature of matter, for example, he followed
Henry More in the latter’s Immortality of the Soul (1659) and noted
that the primary building-blocks of the physical world must be
atoms. Unlike ‘mathematicall points’, matter could not be divided
into infinity, since an aggregation of infinitely small parts, no matter
how small they are, could not make a finite object. Regarding
cohesion, Newton drew on the Cartesian assumption that a solar
‘vortex’ spewed out a rarefied matter that gave rise to the
atmosphere; this in turn ‘pressed down’ on the Earth causing ‘a
close crouding of all the matter in the world’.

Newton

matter that caused gravity, it must rise again in a different form
because (a) otherwise the underground cavities of the Earth would
swell, and (b) the upward rising matter would cancel out the
downward, and there would be no gravity. He also argued that
the ascending matter had to be ‘grosser’ than the descending
matter, otherwise it would impact upon more (i.e. internal) ‘parts’
of large bodies and hence give a more powerful upward than
downward force. This interest in a cyclical cosmos never waned,
and its significance can be seen in his later alchemical and
scientific work.
Even heavenly phenomena could be investigated by experiment.
Notes from Descartes’s Principia about the nature of comets were
followed immediately by Newton’s own observations of the comet of
December 1664, an event whose demands on his time and energy
he would later remember as making him ‘disordered’. Newton
noted that the comet moved north ‘against the streame of the
Vortex’ and he proposed extraordinary experiments for testing the
possible effects of the lunar vortex. Did the Moon’s influence cause
tides? No, he suggested initially, because they would be least when
there was a new moon but this did not happen. Nevertheless, it
might be possible to get a tube of mercury or water and see whether
the height of liquid in the tube was affected by the various aspects of
the Moon.
At each point Newton proposed experiments for deciding central
philosophical questions. No other undergraduate did anything like
it. He put forward a series of tests for determining the specific
gravity of different elements, and also for ascertaining whether the
weight of bodies was affected by being heated or cooled, or by being
moved to different places or heights. Fascinatingly, given his theory
of gravity, he also queried whether the ‘rays’ of gravity could be
reflected or refracted like light. If some of the gravity rays could be
made to strike a horizontal wheel with slats angled at a particular
degree to make it turn like a windmill, or if they were only allowed
to make contact with one half of a vertical wheel in order to make it
30

revolve, then maybe there could be perpetual motion. Similarly, he
posed a series of queries elsewhere in the notebook for deriving
perpetual work from magnetical rays. Perhaps, by transmitting
these rays, a magnet could produce revolutions in a red-hot iron
shaped into sails like those of a windmill? Presumably to test these
views, he purchased a high-quality magnet in 1667 and a short time
later performed a series of highly original experiments with
magnetic filings.

4. Two ideas for perpetual motion machines powered by gravitational
waves, from Newton’s Trinity College ‘Philosophical Questions’
notebook
31

The marvellous years

Questions about the nature of air and water were again prompted
by his reading of Descartes’s Principia Philosophiae, and the latter’s
account of the micro-structures of hard and soft bodies took up
much of his energy. Here, as elsewhere, Newton proposed the use of
Boyle’s air-pump to resolve abstruse theoretical conjectures, many
of them concerning the aether. The refraction of light, for example,
did take place in an evacuated air-pump, so that it had to be caused
by ‘the same subtile matter in the aire & in vacuo’. But was the
extent of refraction the same in different kinds of glass? Boyle had
not considered this, but Newton did, and indeed he had access to an
air-pump in Christ’s College.

Of mind and body
Many entries in the ‘Philosophical Questions’ notebook are
concerned with the nature and precise location of the soul, and the
respective roles that the internal, subjective mind and external
bodies played in experience. From the beginning Newton was
fascinated by what we would call the mind–body problem, and also
by the fact that different people had varied reactions to the same
cause. Under the heading ‘Of sympathie or antipathie’ he noted that
To one pallate that is sweete which is bitter to another. The same
thing smells gratefully to one displeasingly to another . . . Objects of
sight move not some but cast others into an extasie. Musicall aires

Newton

are not heard by all with alike pleasure. The like of touching.

In another section entitled ‘Of Sensation’ (in notes taken from
More’s Immortality), he observed that ‘to them of Java Pepper is
cold’.
In the same series of notes Newton also remarked on the various
locations of the brain that philosophers had invoked as the seat of
the soul. He recorded various phenomena demonstrating that the
brain could be badly damaged without affecting sensation. A frog
would have its ‘sence & motion’ taken away if its brain was ‘peirced’,
but a human would retain the use of his senses unless the piercing
penetrated to the main blood vessels. A man could not, apparently,
see through the hole that a trepan (or drill) made in his head, but
‘the least weight upon a mans brain when hee is trepanned maketh
him wholly devoyd of sensation & motion’.
A key element of his early research programme concerned the
nature of free will, and the associated problem of how the soul was
linked to the rest of the body. Some bodily motion was unconscious.
Under the general heading ‘Of Motion’, Newton recorded that many
human actions were purely mechanical: musicians could play
without thinking, singers sing ‘neither minding nor missing a note’,
32

and people walked without being conscious of how they did so.
Vomiting induced by sticking a whalebone down one’s throat was
another example of an action that was purely mechanical, and it
apparently proved the actions of animals to be ‘mechanicall and
independent of soules’.

In another extraordinary short essay entitled ‘Of Creation’, he
discussed the ‘souls’ of animals, which most philosophers of his day
believed were of a completely separate nature from those of
humans. Newton suggested that there was a sort of primordial
‘irrationall soule’ which when joined to different kinds of animal
bodies made all the various brutes that now existed. In shorthand
(because of the daring nature of his argument), he suggested that to
say that God initially made specific souls for specific species was to
assert that he had done more work than he needed. The differences
between species arose from their instincts, which depended on the
make-up of their bodies. More radically still, he argued that human
souls were basically alike, and that the differences between people
arose merely from distinctions in their constitutions. In a short,
separate entry on God, he noted that neither men nor beasts could
be the result of ‘fortuitous jumblings of attomes’. There would have
been many useless parts, ‘here a lumpe of flesh there a member too
33

The marvellous years

Nevertheless, Newton’s account of the soul involved a vigorous
rebuttal of any purely mechanical explanation for its actions. Like
most of his contemporaries he did not want to be tainted with the
atheistic reputation of mechanical philosophers such as Descartes
and Thomas Hobbes. As the faculty of the soul linked to personal
identity, memory offered significant evidence relating to the springs
of human action. Blows to the head could cause it to disappear
completely, while it could be reactivated by similar events occurring
much later. In an entry entitled ‘Of the soule’ he argued that
memory consisted of more than the action of ‘modified matter’, and
that there had to be a ‘principle’ within us that enabled us to call
something to mind once the original action had ceased. This insight
would be one of the cruxes of Newton’s later natural philosophy.

Newton

much some kinds of beasts might have had but one eye some more
than two’.
The most stunning attempt to distinguish between the actions of
the soul and body began with a series of notes on the nature of the
‘imagination’ (or ‘fancy’) and creativity. The former was a faculty of
the soul that produced images such as those found in dreams and
memory. Newton argued that the imagination was helped by
viewing things ‘in a right posture with the heeles upward’, as well as
by ‘good aire fasting moderate wine’. However, it was ruined by
‘drunkenesse, Gluttony, too much study, (whence & from extreame
passion cometh madnesse), dizzinesse commotions of the spirits’.
‘Meditation’, Newton warned, heated the brain in some ‘to
distraction’, and in others led to ‘an akeing & dizzinesse’. It was
possible to train the imagination to do new things, and from Joseph
Glanvill’s Vanity of Dogmatizing (1661), Newton noted a famous
story of an Oxford scholar who had learnt mind control from
gypsies ‘by heitning his fansie & immagination’.
Some time later than his entry on the Oxford scholar, but
immediately following it in the text, he recorded a series of his own
experiments on imagination and vision. At some point in 1665, he
undertook a series of dangerous experiments on his own sight that
involved staring at the Sun for an extended period of time. These
were reported as subjective experiences, but his detailed description
of a series of trials indicated an objective detachment. After he
had stared at the Sun for some time with one eye, he noted that all
light-coloured objects appeared to be red, while dark objects looked
blueish. At first glance white paper appeared red when looked at
with the damaged eye, but the same paper looked green ‘if I looked
on it through a very little hole so that a little light could come to my
eye’.
The experiment was by no means concluded, for when (as he
thought) the motion of ‘spirits’ in his eye had died down, he could
produce an after-image of the Sun by shutting his eye. There
34

appeared a blue spot, which grew lighter in the middle, gradually
being encompassed by concentric circles of red, yellow, green, blue,
and purple. Varying the experiment under different conditions, he
noted that the spot would sometimes turn red. When he opened his
eye again, he would see colours in exactly the same way as after the
initial experiment. He concluded that the Sun and his imagination
had exactly the same manner of working on the spirits in his optic
nerve and brain. Outside, he looked at a cloud and witnessed the
same reddish effects (‘onely for the most part blacker’) as when he
stared at the white paper, and after a while he could make a spot
‘glitter amidst the dusky red’ when he looked at a cloud that was so
bright his eyes watered.

A new theory of light and colours
Some time after the initial entry on colours, Newton recorded a
series of experiments with prisms on a new page with the same
35

The marvellous years

The fact that this only constituted the first of a series of such
experiments says a great deal about Newton’s uniquely intense
dedication to his task. After giving his eye some respite, he waited
until an hour before dusk and repeated all of the previous
experiment. Now, when he looked with his good eye on white objects
such as paper or clouds, he could see an image of the Sun against
their background, the image being surrounded by ‘a dusky red &
blacknesse’. He found it almost impossible to avoid seeing a
solar image, unless he tried hard to set his imagination on other
tasks. When the image of the sun was just about bearable in either
eye, he could envisage several shapes in the place where the sun had
been, ‘whence perhaps may be gathered that the tenderest sight
argues the clearest fantasie of things visible’. He added: ‘hence
something of the nature of madnesse & dreames may be gathered’.
Such was the enduring power of these trials, that Newton recounted
them in detail to John Locke in 1691, and did so again to John
Conduitt in 1726, telling him that he could still conjure up an image
of the Sun if he put his mind to it.

Newton

heading. With these, he not only refuted the Aristotelian notion of
light and colour, but he also challenged the treatments of the topic
to be found in the recent work of Descartes, Boyle, and Hooke. The
exact date at which he embarked on these investigations is unclear,
but in later accounts, he placed the initial impetus for his research
in his efforts to replicate Descartes’s report of experiments with a
prism in his Dioptrique. In this work, Descartes had argued that the
colours produced by transmitting light through a prism on to a wall
about 50cm away from the prism served to explain the processes
involved in creating a rainbow. At some point, Newton acquired a
prism in order to reproduce this ‘celebrated phenomena of colours’,
but the earliest experimental entries in the ‘Philosophical
Questions’ notebook refer to two instruments.
The very first comment in the new section on colours was a proposal
to test whether a mixture of prismatic red and blue made white.
Already he had criticized older theories that held colour to be a
mixture of black and white, or which assumed that colours arose
through the mixing of shadows with light. Elsewhere in the
notebook, Newton had also subjected to criticism the notion that
light was caused by pressure. This had to be false, for the pressure of
the vortex bearing down on us would make us see a bright light all
the time, while one would be able to see in the dark merely by
running. Finally, he attacked wave theories of light on the grounds
that light travelled in straight lines, whereas waves or ‘pulses’
through an aetherial medium would not. Early on, he became
committed to the idea that light was composed of corpuscles, or
globules, an assumption that ran directly counter to the ‘pulse’ view
outlined in the recently published Micrographia of Robert Hooke.
The key observation was described in the third of a series, in which
he examined a thread – one half coloured blue and the other red –
through a prism. One half, he noted, ‘shall appear higher than the
other & not both in one direct line, by reason of unequall refractions
in the 2 differing colours’. He explained this differential
refrangibility in terms of the underlying speed of the light ‘globules’,
36

assuming that the slower moving rays were refracted differently
from the quicker, and that the blues and purples constituted the
slower rays. He inferred that bodies appeared as red or yellow
whenever the slower rays were absorbed, and were seen as blue,
green, and purple whenever the faster rays were not reflected. This
was the basis of his later, more sophisticated account of how colours
arise in natural bodies in terms of their disposition to ‘exhibit’
certain sorts of rays. As slow or fast moving globules, coloured rays
were permanent features of ordinary light – which was a complex
mixture of them – and individual rays were revealed but not
produced by prismatic refraction. This ran counter to the
universally accepted notion that prismatic colours arose through
‘modifications’ caused by refraction, and threatened both
Aristotelian and standard mechanistic explanations of light and
colour.

Measuring refractions
Newton continued his optical experiments in a so-called ‘chemical’
notebook, in which he entered another essay called ‘Of Colours’.
This was a radically different undertaking, which began with an
account of examining a bi-coloured thread through a prism, but
which then listed a series of highly original experiments on
reflection and refraction. Where contemporaries (who had not
37

The marvellous years

Nor was his work at this point separate from his understanding of
the way in which the eye contributed to the experience of colours,
and he proceeded to undertake a series of ocular experiments every
bit as damaging as the sun-gazing trials. He deformed his eye by
violently pressing it on one side, thus producing a number of
‘apparitions’, and then noted that he made a ‘very vivid impression’
by ‘puting a brasse plate betwixt my eye & the bone nigher to the
midst of the tunica retina than I could put my finger’. Newton
repeated the act on a number of occasions, trying it in the dark,
and also with various degrees of pressure. Needless to say, no other
individual of the period did anything like this.

Newton

known of differential refrangibility) had at most projected refracted
rays a metre or so, Newton showed that different coloured rays had
different indexes of refraction by projecting refracted rays onto a
wall about 7m (22 feet 4 inches) away. In a dark room he let
sunlight in through a tiny hole in the curtains, finding that when
refracted through a triangular prism, the rays produced an oblong
and not a circular shape on the wall. As he had noted before, blue
rays were refracted more than red, although he was also careful to
note that redness and blueness were not intrinsic to rays but were
how specific rays appeared to the eye. With exceptionally precise
measurements, he now determined that differently coloured rays
emerging from the prism had their own specific degrees of
refraction, a fact that no one until then had noticed.
Later in the series of experiments, he described a more complex
arrangement in which the rays emerging from the prism were
further refracted through a second. Blue and red rays each suffered
the same degree of refraction as they had done from the first prism,
and Newton noted that individually coloured rays were not further
modified into other colours when refracted through the second
prism. Introducing a third prism and setting them all parallel, he
allowed emerging rays from all the prisms to overlap with each
other; as he noted, ‘where the Reds, yellows, Greenes, blews, &
Purples of the severall Prismes are blended together there appears a
white’. With these experiments he now had the fundamental
features of what was to be his mature theory of light and colour.
Ignoring his account of globules, he argued that white light was not
a basic entity that gave rise to colours by being ‘modified’. Instead, it
was composed of a number (Newton did not at this point specify
how many) of different primary rays, each of which had its own
immutable index of refraction.
Another significant observation was his analysis of thin coloured
films, a phenomenon originally observed by Hooke. Examining a
flat piece of glass through a lens, placed as close to the glass as
possible, one could see concentric rings of different colours. By
38

considering the radius of curvature of the lens, Newton went as far
as measuring the film of air that existed between the concentric
rings and the plate to nearly one hundred thousandth of an inch. He
developed this analysis in about 1670 or 1671, producing results that
appeared first in his ‘Discourse of Observations’ sent to the Royal
Society at the end of 1675, and then later in his Opticks of 1704. His
main discovery was that the thickness of the film at any point was
proportional to the square of the diameter of each circle. In addition
to this, the difficulty he and others experienced in trying to bring
about contact between the two pieces of glass would later constitute
central evidence for the existence of short-range repulsive forces.

Later, Newton stated that his discovery of chromatic aberration had
put an end to his efforts to improve the grinding of lenses for
refracting telescopes. Descartes had suggested that a lens ground
into either of two conic sections (hyperbola or ellipse) would
produce the clear image that could not be obtained with a spherical
lens (because of the sine law of refraction). Newton himself had
spent many hours attempting to do the same, and had recorded his
results in the Waste Book. But chromatic aberration rendered all
such attempts redundant, as different colours would be refracted
differently and could not be brought to make a sharp image. If
refracting telescopes were out of the question (though Newton did
not entirely give up the idea), then perhaps he could make one that
39

The marvellous years

The second essay ‘Of colours’ also demonstrated vividly that eye
experiments remained a central part of his project. Having
dispensed with a brass plate as a valid tool, he got hold of a ‘bodkin’,
a sewing implement for making holes in fabric, and once more
thrust it into the recess behind his eye ‘as neare to the backside of
my eye as I could’. As before, a number of circles appeared, and as
he put it, they were ‘plainest when I continued to rub my eye with
the point of the bodkin, but if I held my eye & the bodkin still,
though I continued to presse my eye with it,’ the circles would ‘grow
faint & often disappeare until I renewed them by moving my eye or
the bodkin’.

Newton

5. Newton’s drawing of his deformation of his eye by means of a bodkin

used a mirror? Where contemporaries had merely discussed the
theoretical possibility of constructing such an instrument, Newton
went ahead and built a successful version, making every aspect of
the device with his own hands. The metal easily tarnished and the
image was devoid of colour, but it solved the problem of chromatic
aberration and magnified as much as a good refractor. It was a
remarkable achievement, and one for which Newton – reprising his
Grantham role – became famous at Cambridge.
40

Chapter 4
The censorious multitude

The major turn that Newton’s life took after he became a major
fellow of the college in 1668 was to a large extent facilitated by Isaac
Barrow, who had by now recognized Newton’s potential. He
thanked Newton (although not by name) for help in revising his
Eighteen lectures on optical phenomena of 1669, and Newton
almost certainly attended his Lucasian lectures on geometrical
optics in 1667 and 1668. Barrow was presumably unaware of the
radical nature of Newton’s work in that area but with his support,
Newton was elected as his successor in the Lucasian Chair in
September 1669.
Early in 1669 Barrow had shown Newton a copy of Nicholas
Mercator’s Logarithmotechnia, published at the end of the previous
year. Mercator had discovered a way of deriving values for logarithms
by using infinite series; Newton claimed later that when he read the
work, he had assumed (wrongly) that Mercator had uncovered the
generalized binomial theorem for expanding polynomials with
fractional powers. In any case, seeing Mercator’s book and realizing
that Mercator had begun to ‘square’ terms to produce infinite series
prompted him to compose a remarkable mathematical tour de
force, now known as ‘On analysis by infinite series’ (or ‘De Analysi’).
He did not specify the binomial theorem in this work but, amongst
other treasures, laid out a number of infinite series that
approximated to values for sin x and cos x, along with techniques for
41

Newton

integrating the cycloid and the quadratrix. He announced that the
methods of tangents and quadratures were inverse techniques, and
drew from the October 1666 tract to offer a powerful basis for his
method of fluxions. He would draw from ‘On analysis’ in two major
mathematical letters written to Leibniz in 1676.
Barrow communicated this work to the London mathematician
John Collins at the end of July 1669, revealing Newton’s authorial
identity a month later. Infinite series were all the rage, and via
Collins, Newton’s achievements, as well as the actual text, came to
the attention of other mathematicians. In fact, in November
Newton met Collins in London, where they discussed his reflecting
telescope, series expansions, harmonic ratios, and the fact that
Newton ground his own lenses. However, Collins noted that he was
unwilling to disclose the general method underlying his work. At
this time Barrow asked Newton to comment on the Algebra of
Gerard Kinckhuysen, which Collins had recently translated.
Newton’s extensive remarks were never published but in any case
he exhibited what Collins thought was a bizarre unwillingness for
his name to be attached to the piece. He made it clear to Collins in
September 1671 that he wanted his work to appear anonymously – if
it appeared at all – and he had no desire ‘to gain the esteeme of one
ambitious among the croud to have my scribbles printed’. This
attitude would govern his relations with potential audiences for his
work for the next three decades.
Newton’s Lucasian lectures on geometrical optics differed
dramatically from those given by his predecessor. He employed a
barrage of experiments, prisms, and lenses to corroborate his theory
of the heterogeneity of white light and placed a major emphasis on
the mathematical precision and certainty that attended his work,
urging that natural philosophers should become geometers and
should stop dealing with knowledge that was merely ‘probable’.
Here was Newton’s first public pronouncement that natural
philosophy could reach an absolute level of certainty and should be
based on mathematical principles.
42

The cause of Newton’s disillusionment was his first contact with an
international audience. Collins had already been informed by
Newton of the existence of his reflector, and the topic was ‘live’
again at the end of 1671 when Barrow delivered a new version of the
instrument to the Royal Society. It was much admired by the
fellows, and was examined in some detail ‘by some of the most
eminent in Opticall science and practise’, as the Secretary of the
Society, Henry Oldenburg told him. Oldenburg told Newton that a
description of the instrument’s construction and capacity had been
sent to Christiaan Huygens at Paris, ‘to prevent the arrogation of
such strangers, as may perhaps have seen it here, or even with you
in Cambridge’.
In reply Newton adopted his standard aloofness about his own
invention, telling Oldenburg he had had the device in Cambridge
for some years without making any great song and dance about it.
He added advice on how to produce an alloy for the mirror and
43

The censorious multitude

At this point Newton could have published work that would have
stamped him as one of the most fertile scientists, and certainly the
most brilliant mathematician the world had seen. Collins spent
some time pushing him into publishing both ‘On analysis’ and a
version of his optical lectures, and Newton expended a great deal of
effort revising them, expanding the first (in early 1671) into a new
treatise on methods of series and fluxions. He also rewrote his
optical lectures in the second half of 1671, producing a new version
that differed from the earlier one in that it suggested that one
should measure refractions and reflections before discussing the
nature of colours. However, when Collins prompted him again in
April 1672, Newton told him that he had been thinking of preparing
a joint publication of his optical and mathematical work, but had
desisted, ‘finding already by that little use I have made of the Presse,
that I shall not enjoy my former serene liberty till I have done with
it’. Nevertheless, at this time his name did appear as the editor of a
book on geography by Bernard Varenius, a work to which he later
admitted he had added little.

Newton

6. A sketch made by a member of the Royal Society of Newton’s
reflecting telescope presented to them by Isaac Barrow at the end of
1671

thanked the Society for electing him a fellow. He continued his pose
of modesty in accepting the offer of a fellowship of the Society,
offering to convey to them whatever his ‘poore & solitary
endeavours’ could do to benefit their activities. Nevertheless, a
further letter revealed that he had been prompted into constructing
the reflector by what was in his judgement ‘the oddest if not the
most considerable detection which hath hitherto been made in
44

the operations of nature’. Oldenburg duly received Newton’s
epoch-making paper early in February 1672.

Newton at the Royal Society

In his February paper, Newton began in the historical narrative
style, relating that – in the midst of trying to grind non-spherical
lenses – he had bought a prism in 1666 and passed sunlight
through it in a dark room on to a wall 22 feet away in order to test
the ‘phenomena of colours’. Expecting to see a circular image
according to the laws of refraction, he had been ‘surprised’ to see
instead that it was ‘oblong’. According to his story, he gradually
removed various explanations for the elongated ‘spectrum’,
including the thickness or unevenness of the glass, and made a
precise measurement of the experimental set-up. The difference
between the angle made by the rays entering the prism (31′ ), and
45

The censorious multitude

In the years since it had been founded in 1660, the Royal Society
had fashioned what was effectively an official position regarding the
best way to perform and write up experiments. To a large extent,
this was based on the approach adopted by Robert Boyle, who in his
writings had suggested that authors adopt a ‘historical narrative’
style. This involved authors describing what they had actually done
on a particular occasion in as detailed a manner as possible.
Where they could, writers were to avoid any reference to hypotheses
that were experimentally untestable, and they were not to make
over-hasty general statements about how nature would behave in all
similar cases. They were also to be modest about what they claimed,
to the extent that they should not claim greater certainty for their
views than was warranted by the evidence. Time and the replication
of phenomena by many other people on a number of occasions
would prove the truth or otherwise of any statement. Boyle thought
that some mathematically inclined natural philosophers were
over-confident in applying mathematical techniques to the natural
world, and in claiming an unwarranted degree of certainty for their
work.

Newton

by those leaving (2° 49′ ), was too great to be explained by the
conventional laws of refraction.
‘At length’, he noted, he came to what he termed the experimentum
crucis (crucial experiment, a term derived from the Baconian
phrase instantia crucis). This was a refined if obscurely rendered
version of the two-prism experiment described in the most mature
of his essays on colours. He took two boards, both with very small
holes in them, placing one next to the window (where the first prism
was placed), and a second, 12 feet away from the window. Turning
the first about its axis, he allowed different coloured rays to pass
through the hole in the second board and onto a second prism next
to it on the other side. As would become much clearer later, the
experiment was supposed to show that, although they all had the
same angle of incidence to the second prism, each individual
coloured ray experienced the same degree of refraction emerging
from the second as it had from the first. The degree of refrangibility
was not modified by the second prism and thus every coloured ray
had an intrinsic ‘predisposition . . . to suffer a particular degree of
refraction’. Chromatic aberration, he commented, placed limits on
the sort of precision that could be gained from refracting telescopes.
Halfway through the text Newton gave up on the historical
narrative method, claiming that continuing in that vein would
make his paper ‘tedious and confused’. Natural philosophers, he
said, would be amazed to find that the theory of colours was a
‘science’ based on mathematical principles; it was not hypothetical,
but was absolutely certain, being based on incontrovertible
experiments. In the remainder of the paper he offered to lay down
the ‘doctrine’ of his theory, adding one or two experiments to serve
as illustrations. A ray of a particular sort ‘obstinately retained its
colour’ when passed through successive prisms, ‘notwithstanding
my utmost endeavours to change it’. Most wonderful of all, he
exulted, was the fact that white light was composed of all the
primary rays being brought together. His theory could explain the
colours of all natural bodies, which were seen as a particular colour
46

because of their tendency to reflect certain rays and not others. He
concluded by saying that it was much more difficult to determine
what light actually was, or how it was refracted, or ‘by what modes
or actions it produceth in our minds the Phantasms of Colours’,
although he offered a hostage to fortune by asserting that it could
perhaps no longer be denied that light was corporeal (i.e. made up
of bodies). However, the last claim was not essential to his
argument, he said, and he would not ‘mingle conjectures with
certainties’.
The essay was not merely the most radical challenge to accepted
views about optics in modern history, but was a clear statement
about what Newton took to be the proper way to investigate and
justify scientific claims. In reply, Oldenburg remarked that the
fellows had considered the paper with ‘a singular attention and an
uncommon applause’, and had asked for it to be printed in the
Philosophical Transactions. He also mentioned that the Society had
decided that some of its members should attempt to repeat the
experiments described in the paper, as well as some other relevant
ones. Newton replied that he had sent his paper to the Society on
47

The censorious multitude

7. A reproduction of the crucial experiment, from the 2nd French
edition of Newton’s Opticks

account of their being the ‘most candid & able Judges in
philosophicall matters’, and remarked that he deemed it a ‘great
‘privilege that instead of exposing discourses to a prejudic’t &
censorious multitude (by which many truths have been baffled &
lost)’, he could now ‘with freedom’ turn his attention ‘to so judicious
& impartiall an Assembly’.

Newton

The trouble with hypotheses
The combined publication of the description of the telescope and
the paper on light and colours made him famous. A number of
contemporary philosophers, most notably Christiaan Huygens,
expressed their approval. However, the Royal Society’s star
performer, Robert Hooke, wrote to Oldenburg within a week to say
that he had grave reservations about the theory. Although he agreed
that the phenomenon was true, he did not believe that differential
refrangibility could only be explained by Newton’s theory of the
heterogeneity of white light, nor did he agree that it showed that
light was corporeal. Hooke announced that he had found similar
effects before, and he could not agree that Newton’s theory of white
light was as certain as Newton made it out to be.
Hooke’s own hypothesis, namely that light was a pulse or motion
transmitted through an undifferentiated and invisible medium –
with colour being a modification of light caused by refraction – was,
he asserted, based on hundreds of experiments. If Newton really did
have a single compelling crucial experiment that proved his own
thesis, then Hooke would readily concur with Newton’s theory.
However, he could think of numerous other hypotheses that would
also explain what had happened. Why should all the motions that
make up colour be in the white light before it hit the prism? There
was no necessity for this to be the case, any more than there was
that the sounds were ‘in’ the bellows that later issued from the pipes
of an organ. Newton’s theory was merely a hypothesis, if a ‘very
subtill and ingenious one’, and not nearly so certain as a
mathematical demonstration.
48

Newton’s lengthy response to Hooke of June 1672 used a wealth of
data from his optical lectures as well as from his laboratory
notebook, and in itself was a major contribution to optics. The reply
started with a haughty rebuke about Hooke’s behaviour. He should
have ‘obliged’ Newton with a private letter, while the ‘hypothesis’
Hooke had ascribed to him was not the one Newton had expressed
in his paper – for nothing hung on whether light were a body or not.
Ignoring ‘hypotheses’, which he despised, Newton had spoken of
light ‘in generall termes, considering it abstractedly as something or
other propagated every way in straight lines from luminous bodies,
without determining what that thing is’.

Hooke could scarcely mistake the tone. In a letter to a senior
member of the Royal Society he noted that he had since performed
further experiments with prisms and coloured rings, as Newton had
suggested, but remained unconvinced by Newton’s theory.
Nevertheless, he added that he was sorry if Newton had been
offended by what he had written, since it had never been meant for
his sight. Hooke stressed that he did have good evidence for his
views, and indeed he had produced diffraction experiments which
49

The censorious multitude

Newton then launched a direct assault on Hooke’s wave theory of
light, using ar