1 From Galileo to Daniel Bernoulli

Our first five remarkable physicists were born in the 137 years from 1564 to 1700.

They came from Italy, Germany, the Netherlands, England and Switzerland.

Galileo Galilei (1564–1642)

The great scientist we know as Galileo was born in Pisa on February 15,

1564. He was the eldest son of the notable composer, lutenist and musical

theorist Vincenzio Galilei, of a long-established Florentine family, and his

wife Giulia (n ´ee Ammananti), a native of Pisa who considered herself

socially superior to her husband. They had five or six other children. Like

Dante, Leonardo, Michelangelo and other great Italians of that period he

is universally known by his first name rather than by his family name. In

1574 the family moved to Florence. After four years of education in the

Camaldolese abbey of Vallombrosa on the upper Arno, Galileo was expecting

to make his career in the church. However, his father decided otherwise

and arranged for his son to live in Pisa with a cousin, who would train him

as a wool merchant. Before long it became clear that the young man was

unusually able and so, at the age of seventeen, he entered the University

of Pisa, training to become a doctor in accordance with his father’s wishes.

However, he was dissatisfied with the lectures provided, left after four years

without taking a degree, and when he returned home it was to work on mathematics.

Apparently he was introduced to the subject by Ostilio Ricci, said

to have been a student of Tartaglia’s, who was mathematician at the court

of the Grand Duke of Tuscany. Galileo took pupils and gave some public

lectures on mathematics in Siena and Florence. In 1587 he visited the leading

Jesuit astronomer and mathematician Father Christopher Clavius at

the Gregorian University in Rome, who was interested in his first research

papers, one on the determination of centres of gravity of parabolic conoids

and another on an ingenious balance (La bilancetta) he had designed for

determining specific weights with precision.

In 1589 Galileo was appointed to a teaching post in mathematics at

the priest-dominated University of Pisa, at that time something of an intellectual

backwater. During his time there he wrote, but did not publish, a

2 From Galileo to Daniel Bernoulli

paper called De motu, about the flight of projectiles and other dynamical

problems. Three years later he moved to a professorship in Padua, one of

the leading universities of Europe, where Copernicus had taught and Dante

had studied. Padua, in the Venetian Republic, offered a far more congenial

atmosphere than Pisa. Professors were not well-paid; they were expected to

supplement their modest salaries by private tuition. Galileo was an excellent

teacher, whose students were devoted to him. He presided over a lively

household of young men to whom he taught practical subjects such as military

architecture, elementary astronomy and perspective. He also ran a

small workshop to manufacture scientific instruments, and, as a result of

his entrepreneurship, he became a man of means. Even so, after the death

of his father in 1591, he found it difficult to meet his responsibilities towards

his improvident brother, who frequently came to him for money, also his

sisters needed dowries if they were to marry, so that at times he ran the risk

of being arrested for debt.

In the nearby city of Venice Galileo found friends in the nobility. The

most important of these was Gianfrancesco Sagredo, a confirmed bachelor,

who seemed to have been exhausted by dissipation in his youth. However,

as he grew older he turned to tamer pursuits, including wild parties at his

country estate on the River Brenta. Sagredo was interested in science and

he formed a lasting friendship with Galileo, which they continued by correspondence

when the Doge sent Sagredo to Aleppo for three years in a

Galileo Galilei (1564–1642) 3

diplomatic capacity in 1608. Galileo never married but he formed a lasting

relationship with a twenty-one-year-old Venetian serving-woman named

Marina Gamba, said to be beautiful, hot-tempered, lusty and probably illiterate.

Galileo’s shrewish mother thoroughly disapproved of her and caused

trouble. Marina had three children by Galileo: Vincenzo, Virginia and Livia.

Galileo took an interest in their son’s education; once they were old enough

he placed their daughters in the convent of San Matteo in Arcetri, on the

outskirts of Florence.

Galileo was already coming round to the view that the heliocentric

system of Copernicus was much more plausible than the geocentric system

of Aristotle and Ptolemy. In this he was influenced by the German

astronomer Johannes Kepler, whose profile comes next.Amongother things,

Galileo invented a machine for raising large amounts of water from aquifers,

an air thermoscope and a computing device for geometrical and ballistic

purposes described in his first printed work Le operazioni del compasso

geometrico e militare (Padua, 1606), which described the operation of

a lightweight military compass he had designed in collaboration with a

Venetian toolmaker. In pure science his research led him about 1602 to the

discovery of the isochronicity of the pendulum and to the preliminary but

wrong discussion of the law of falling bodies. In 1609 he was the first to

apply the newly invented telescope to astronomical observations, revealing

the mountains on the moon, numerous stars invisible to the naked eye, the

nature of the MilkyWay and four of Jupiter’s satellites (named the Medicean

stars). These sensational discoveries were described in his Sidereus nuncius

(The Sidereal Messenger) (Venice, 1610), one of the most important scientific

books of the seventeenth century, which at once made Galileo famous

all over Europe. The popular excitement was overwhelming.

The Pope had declared the first year of the new century to be a Jubilee

year. It was to be a year of celebration but also of renewed determination

to stem the tide of reform. The greatest intellectual of the church of Rome,

Cardinal Robert Bellamine, led the drive to stamp out heresy. One of the

first victims was the Dominican friar Giordano Bruno, who was imprisoned,

tortured and burnt at the stake for his beliefs. He conjectured that ‘There

are countless constellations, suns and planets; we see only the suns because

they give light; the planets remain invisible, for they are small and dark.

There are also numberless earths, circling round their suns.’

Students came from many parts of Europe to sit at Galileo’s feet,

including French, English, German and Polish nobility, also the Swedish

King Gustavus Adolphus. The new Grand Duke of Tuscany, young Cosimo

4 From Galileo to Daniel Bernoulli

de Medici, was one of his former pupils. In 1610, feeling he was not sufficiently

appreciated in the Venetian Republic, Galileo relinquished his chair

at the University of Padua after eighteen years of great creative activity and

accepted an appointment as chief mathematician and philosopher at the

court of the Medicis. Back in Florence, he devoted his entire energy to scientific

research under the benevolent protection of the Grand Duke. In his

social circle, the place of Sagredo was taken by a wealthy and accomplished

young patrician named Filippo Salviati. His country retreat Le Selve in the

hills above the lower Arno became a centre for philosophical discussions,

in which Galileo was surrounded by young disciples.

Galileo decided it was time for another visit to Rome, this time as a

kind of scientific ambassador, sponsored by the Grand Duke. Galileo was

received by Pope Paul V, the successor of Clement VIII, and generally lionized.

He set about promoting the new cosmology by demonstrating the latest

discoveries. These included the phases of the planet Venus, the composite

structure of Saturn and the existence of sun-spots, all described in his Istoria

e dimostrazioni intorno alle macchie solari (Treatise on Sunspots) (Rome,

1613). However, the Jesuits at the Gregorian University continued to cling

to the old cosmology. One of them was Father Clavius, on whom he had

called twenty-four years earlier; the German mathematician took note of

Galileo’s discoveries, but refused to embrace Copernicanism.

Galileo found an important new patron in Federico Cesi, an influential

young nobleman who possessed an enormous curiosity and the courage to

break the confines of his aristocratic upbringing. When he was only eighteen

Cesi had established the Accademia dei Lincei, arguably the first successful

scientific society to be founded in the seventeenth century. The stated

aim of the Lincei was to bring together ‘philosophers who are eager for real

knowledge, and who will give themselves to the study of nature, and especially

to mathematics. At the same time, it will not neglect the ornaments

of elegant literature and philology, which like graceful garments, adorn the

whole body of science.’ Initially the society had only four members, all nonscientists

and all under thirty years of age; there hung about the Lincei a

certain air of the occult and of pseudo-science, even the taint of scandal.

The society held its meetings in Cesi’s palace, which contained a splendid

library, including many proscribed books, and a collection of scientific

instruments, specimens and curiosities. Its early fame rested mainly on

Galileo’s participation; later it gave him much-needed support, stimulus

and encouragement. Cesi was too powerful to have to worry about what the

Jesuits at the Gregorian University thought.

Galileo Galilei (1564–1642) 5

Galileo was becoming more and more audacious in pointing to the

incompatibility of the new celestial phenomena with traditional astronomy.

He openly confessed his Copernican conviction, already stated in a letter to

Kepler, at the same time as he successfully attacked current views on hydrostatics

in his Discorso intorno alle cose che stanno in su l’acqua (Bodies

in Water). Increasingly Galileo had to defend his discoveries and opinions

against numerous attacks from scientific opponents and jealous academic

enemies.Aconspiracy among the latter aiming at Galileo’s downfall led first

to an abusive sermon against him in Florence in 1614. There were signs

of paranoia in his reaction, although the enemies were real enough. The

most powerful of these was Cardinal Bellarmine, the persecutor of Giordano

Bruno, who warned him not to defend the Copernican system in public. As

a result, he wrote a letter to Christina, the mother of the Grand Duke, giving

his carefully considered opinions about the proper relation between science

and religion; this Letter to the Grand Duchess Christina was not published

until 1636.

Galileo was already fifty years of age. He was suffering from arthritis,

a condition of long standing, and from pains in the chest and kidneys. On

his return from Rome he first took advantage of Salviati’s villa Le Selve to

recuperate before settling down in a modest villa of his own, at Bellosguardo,

overlooking Florence and not too far from Arcetri where his daughters lived

inside their convent. However, it is hardly surprising that the following

years saw some decline in his scientific activity. He mainly occupied himself

with computing tables of the motion and eclipses of the moons of Jupiter,

which could be used to determine longitude at sea. He tried in vain to sell

this idea to the Spanish and Dutch governments. In 1618 he was involved in

a bitter argument over the nature of comets, which lost him the sympathy

of his former supporters among the Roman Jesuits. A result of this controversy

was the polemical work Il saggiatore (The Assayer) (Rome, 1623)

in which Galileo expressed his thoughts on epistemological and methodological

questions, stressing the necessity of quantitative experiments and

observations and the strength of hypothetical–deductive reasoning.

In 1623 one of his former supporters, Cardinal Maffeo Barberini,

became Pope Urban VII, and, after a fourth visit to Rome, Galileo felt himself

encouraged to begin with the composition of a major work on astronomy,

planned many years before and finally published under the title Dialogo

sopra i due massimi sistemi del mondo (Dialogue Concerning the Two

Chief World Systems). This was a technical account in the form of a dialogue

among a supporter of the Aristotelian–Ptolemaic tradition named

6 From Galileo to Daniel Bernoulli

Simplicio, a youthful enquiring mind named Sagredo and an advocate of the

new astronomy named Salviato. Galileo had tried to safeguard himself by

letting Simplicio prevail, and the book was published with the imprimatur

of the ecclesiastical authorities. Nevertheless the strength of Salviato’s arguments

was evident.

The initial reception of the book was generally favourable, but it

gave Galileo’s enemies the opportunity they had been waiting for. The

Pope thought the imprimatur should never have been granted and tried

to have the book suppressed, but it was too late. He decided that Galileo

must stand trial and summoned him to Rome. The Grand Duke was powerless

to shield Galileo from the wrath of the Pope. For reasons of health

Galileo asked for the proceedings to be held in Florence. This was refused

but, as a concession, when he arrived in Rome, instead of being committed

to prison while awaiting trial, he was allowed to live in the Tuscan embassy.

Formally the charge against him was one of disobedience. His accusers

maintained that Bellamine in 1616 had formally admonished Galileo not

to promote Copernicanism in public; Galileo denied this, documentation

was lacking and Bellamine was no longer alive to give evidence. During

the trial the ailing Galileo was imprisoned in the Vatican, until eventually,

more dead than alive and under threat of torture, he was forced solemnly

to abjure his Copernican convictions before the Congregation of the Holy

Office, before being sentenced to life imprisonment and punished in other

ways.

Initially he was confined to the palace of the Archbishop Ascanio

Piccolomini of Siena, a man of broad cultural interests, where he was treated

as an honoured guest. Before long, however, the Pope’s agents reported

that the episcopal palace did not keep him sufficiently isolated and he was

allowed to move to his villa in Bellosguardo. In 1631, finding the journey

from there to see his daughters too much, Galileo proposed to move to

a house in Arcetri itself. The Pope agreed that he could do so, although

still effectively under house arrest, since he was not even allowed to go to

nearby Florence without permission, which was sometimes withheld. His

younger daughter Livia suffered from depression but Galileo was to find

great comfort in the company of his elder daughter Virginia in his declining

years. In the simple beauty of the weekly letters she sent him, as ‘Suor

Maria Celeste’, we can follow her efforts to comfort him and lift his spirits;

unfortunately his side of the correspondence has not survived. Sadly, she

died from dysentery not long after he had arrived in Arcetri, at the age of

thirty-three.

Galileo Galilei (1564–1642) 7

Galileo’s own health was seriously threatened; there was a troublesome

hernia and palpitations of the heart, and he also suffered from insomnia

and melancholia. He continually heard his beloved daughter calling him.

The Florentine Inquisitor was right to believe that the aged Galileo would

never again attempt to promote Copernicanism. In fact, Galileo went further

by stating that the falsity of Copernicanism must not on any account

be called into doubt, especially by Catholics. All Copernican conjectures,

he wrote, are removed by the most solid arguments from God’s omnipotence.

He had resigned himself to the fact that his own part in the campaign

to establish Copernicanism was over, although his personal convictions

remained the same and many were protesting against the injustice of his

condemnation and sentence.

Galileo engaged in new research, although hampered both by cataracts

and by glaucoma, ending in complete blindness, and by the constant supervision

of the Inquisition. He succeeded in finishing his final and most important

work, the Discorsi e dimostrazioni matematiche intorno a due nuove

scienze (Discourses on Two New Sciences) (Leyden, 1638), which was, significantly,

published beyond the reach of the Inquisition. This work, containing

among other things the proof of the laws governing the fall of a body

in a vacuum, the principle of the independence of forces and the complete

theory of parabolic ballistics, was destined to become one of the cornerstones

upon which Huygens and Newton one generation later built classical

mechanics. The laws of fall made it possible to study accelerated motion.

Simplicio, Sagredo and Salviati reappear to debate the arguments in another

dialogue like the one he had used in 1632; Galileo’s fondness for this manner

of presentation may have come from his father, who in 1581 had published

a Dialogo della musica antica e moderna. Galileo died at Arcetri during

the night of January 8, 1642. He was buried privately in Santa Croce, the

great church where so many famous Tuscans lie, but not in the Galilei

family tomb, for fear of Papal disapproval. No monument to his memory

was erected until 1737, when he was re-interred and the skeleton of a young

woman was found beneath his in the original grave; it is thought that this

could have been his beloved daughter.

Galileo had a versatile mind. He was an accomplished amateur

musician and a master of the vernacular language; his polemical work Il

saggiatore is one of the Italian classics. He occupied himself with almost

every branch of physics, but is chiefly remembered for the example he gave of

the efficacy of the hypotheco-deductive method combined with quantitative

experiments. In general history too he occupies an important place because

8 From Galileo to Daniel Bernoulli

of his personal fate, which was an important factor in the widening fissure

between natural science and the spirituality of the counter-Reformation.

The last traces of official anti-Copernicanism were not removed until 1822.

While geocentrism was the official doctrine, there was some latitude for

teaching heliocentrism as a working hypothesis in schools and universities

where Jesuits were in control.

Johannes Kepler (1571–1630)

Kepler was a near-contemporary of Galileo but his life-story was very different,

as was his family background. He was born in the small Lutheran

town ofWeil der Stadt, near Stuttgart, on December 27, 1571. Judging by the

account Kepler wrote of his early life, he seems to have had a most miserable

childhood. He described his father Heinrich as ‘criminally inclined, quarrelsome,

liable to a bad end’ and his mother Catharina (n´ee Guldenmann),

as ‘small, thin, swarthy, gossiping and quarrelsome’, adding that ‘treated

shabbily, she could not overcome the brutality of her husband’. When he

was three years old, his father joined a group of mercenary soldiers to fight

the Protestant uprising in Holland. His mother followed her husband to

Flanders. The children were abandoned to the care of grandparents who

treated them roughly. When their parents returned in 1576 the family, in

disgrace because of Heinrich’s part in the persecution of Protestants, had

Johannes Kepler (1571–1630) 9

to leave Weil for nearby Leonberg, in the Grand Duchy of Wu¨ rttemberg.

Heinrich rejoined the infamous Duke of Alba’s military service for a few

more years; by 1588 he had abandoned his family forever.

The future astronomer was a sickly child, with thin limbs and a

large pasty face surrounded by dark curly hair. He was born with defective

eyesight – short-sighted in one eye, multiple vision in the other. His stomach

and gall bladder gave constant trouble; and he nearly died from smallpox.

He began his education at the German Schreibschule in Leonberg but soon

moved to the Latin school, there laying the foundation for the complex

Latin style displayed in his later writings. After a period of ‘hard work in

the country’, during which he did not attend school at all, he entered the

Adelberg monastery school at thirteen; and two years later enrolled at the

more senior Maulbronn, one of the preparatory schools for the Protestant

University of Tu¨ bingen. In October 1587 Kepler formally matriculated at

the university; but because no room was available at the Stift, the seminary

where, as a student supported by the enlightened Duke of Wu¨ rttemberg, he

was expected to lodge, he continued at Maulbronn for another two years.

In September 1588 he passed the baccalaureate examination at the university,

although he did not actually take up residence there until the following

year. He was unpopular with his fellow-students, who gave him a hard

time.

At Tu¨ bingen, Kepler’s thought was profoundly influenced by Michael

Maestlin, the professor of mathematics and astronomy. Although Maestlin

was at best a very cautious Copernican, the 1543 De revolutionibus he

owned is probably the most thoroughly annotated copy extant; he edited

the 1571 edition of the Prutenicae tabulae and used them to compute his

own Ephemerides. Kepler was an exemplary student; and, when he applied

for a renewal of his scholarship, the university senate noted that he had ‘such

a superior and magnificent mind that something special may be expected of

him’. Nevertheless, although Kepler himself wrote concerning his university

education that ‘nothing indicated tomea particular bent for astronomy’,

in student disputations he often defended Copernicanism.

In August 1591 the twenty-year-old Kepler received his master’s

degree from Tu¨ bingen and thereupon entered the theological course.

Halfway through his third and last year, however, there occurred an event

that completely altered the direction of his life. The teacher of mathematics

and astronomy at the Lutheran school in the Styrian capital of Graz

had died, and Tu¨ bingen was asked to nominate a replacement. Kepler was

chosen, and, although he was reluctant to abandon his intent of becoming

10 From Galileo to Daniel Bernoulli

a Lutheran pastor, at the age of twenty-two he embarked on the career

destined to immortalize his name.

Kepler arrived in southern Austria in April 1594 to take up his duties

as teacher and as provincial ‘mathematicus’. In the first year he had few

pupils in mathematical astronomy and in the second year none, so he was

asked to teach Virgil and rhetoric as well as arithmetic. However, the young

Kepler made his mark in another way; one of the duties of the mathematicus

was to produce an annual calendar of astrological forecasts. His first

calendar, for 1595, contained predictions of bitter cold, peasant uprisings

and Turkish invasions. All were fulfilled, to the great enhancement of his

local reputation. Five more calendars followed in annual succession, and

later, when he had moved to Prague, he issued prognostications for the

years 1602 to 1606. Later still Kepler produced a series of calendars from

1618 to 1624, excusing himself with the remark that, when his salary was

in arrears, writing calendars was better than begging.

Kepler’s attitude to astrology was mixed. He rejected most of the commonly

accepted rules and repeatedly referred to astrology as the foolish stepdaughter

of astronomy. However, casting horoscopes provided welcome

supplementary income and later became a significant justification for his

office as imperial mathematicus. Moreover, the profound feeling he developed

for the harmony of the universe included a belief in a powerful accord

between the cosmos and the individual. These views found their fullest

development in the Harmonicae mundi, published towards the end of his

life.

Meanwhile, just over a year after his arrival in Graz, Kepler’s fertile

imagination hit upon what he believed to be the secret key to the universe –

the number, dimensions and motions of the planets. This theory, published

in his decisively pro-Copernican treatise Mysterium cosmographicum of

1596, was based on the idea that the five regular solids space out the six

known planets; each planetary orbit is circumscribed by a regular solid

and has inscribed in it the solid of the next planet below. Although the

principal idea was erroneous, Kepler established himself as the first (and,

until Descartes, the only) scientist to demand physical explanations for

celestial phenomena.

Kepler had submitted his manuscript to the scrutiny of the Tu¨ bingen

senate because his publisher would not proceed without its approval.

Although they raised no objection to the publication, he was requested to

explain his discovery in a clearer and more popular style. When it appeared,

the reasons for abandoning the Ptolemaic in favour of the Copernican

Johannes Kepler (1571–1630) 11

system were set forth with remarkable lucidity. Kepler sent copies to various

scholars, including Galileo and the great Danish astronomer Tycho Brahe.

Its faults notwithstanding, Mysterium cosmographicum thrust Kepler into

the front rank of astronomers. Seldom has so wrong a book been so seminal

in directing the future course of science.

Meanwhile Kepler’s friends arranged his marriage to Barbara

Mu¨ ehleck, the eldest daughter of a wealthy mill-owner. She was two years

younger than Kepler and had been widowed twice. Early in 1596 Kepler

sought her hand, but her family thought him beneath her and the negotiations

were difficult and protracted. They insisted that the modest fortune

she brought to their marriage be reserved for their children. The wedding

took place the next spring, under ominous constellations, as Kepler noted in

his diary. He soon realized that his wife would never understand anything

of his work – ‘simple of mind and fat of body’ was Kepler’s later description

of her. Of their five children, one boy and one girl survived to adulthood.

The numerous Protestants in Graz remained unmolested by their

Catholic rulers until 1598. Then, on a day in late September, all the teachers,

including Kepler, were abruptly ordered to leave town before sunset.

Although Kepler was allowed to return, unlike his colleagues, conditions

remained tense. In the second half of the sixteenth century the Czech kingdom

of Bohemia experienced great prosperity under the Habsburg emperor

Rudolph II, who made Prague his capital and attracted to it a galaxy of artists,

scholars, alchemists and magicians. In August 1599 Kepler learned that the

wealthy, aristocratic Brahe had been appointed imperial mathematicus by

Rudolph, with an exceptionally generous salary. Early in 1600, Kepler made

an exploratory visit to the observatory Brahe had established at Benatky

Castle, near Prague. It was equipped with scientific instruments of the highest

quality, although telescopes had not yet come into use. Kepler respected

the outstanding precision of Brahe’s observational data and expected that

he would be given access to them. However, Brahe treated him as a novice,

rather than an independent investigator, and refused to share his results.

The two astronomers soon quarrelled, but before Kepler returned to Graz

they had achieved some degree of reconciliation.

In Graz, by this time, the counter-Reformation was taking effect, and

in August 1600 Kepler and other Protestants were expelled from the predominantly

Catholic city. Already deeply depressed by the death of his first

two children, he decided to go back to Prague, with his family. When they

arrived, Kepler found that Brahe’s chief assistant, Longomontanus, had just

died. Kepler was appointed in his place, but Brahe still refused to share his

12 From Galileo to Daniel Bernoulli

observational data, and there was further friction when payment of Kepler’s

salary was delayed. He returned to Graz in April 1601 on an extended visit

occasioned by his father-in-law’s death and the need to safeguard his wife’s

interests.

Eventually the differences between the two astronomers were patched

up; then in the autumn Brahe was suddenly taken ill and towards the end

of October he died. Almost at once Kepler was appointed to succeed him

as imperial mathematicus, although five months passed before he received

his first instalment of salary. One of his various duties was to complete

Brahe’s work on what became known as the Tabulae Rudolphinae, giving

the positions of a great many stars and perpetual tables for calculating the

positions of the planets on any date in the past or future. This task, involving

enormous quantities of laborious calculations, was by no means congenial

to Kepler, and, even when it had been completed, publication was delayed,

as we shall see.

Kepler’s main interest remained more in theoretical astronomy. He

began to speculate that the solar system might be held together by magnetic

attraction. Although this was not right, it represented an imaginative leap

in the direction of universal gravitation. He also began to consider the possibility

that the planetary orbits might be elliptic, with the sun at one focus,

and here of course he was right. These ideas appeared in his next important

book, the Astronomia nova of 1609. Unfortunately publication was held

up, partly by the lack of imperial financial support but also by opposition

from the heirs of Brahe. They took away Brahe’s scientific instruments and

allowed them to decay unused. They also tried to remove the vital records

of his observations, but Kepler managed to prevent this.

Despite poor eyesight, Kepler was one of the pioneers of research into

optics. He found a good approximation to the law of refraction; Descartes,

the discoverer of the precise law, said that Kepler was his true teacher in

optics, who knew more about this subject than did any of those that preceded

him. This research was published in his Dioptrice of 1611, which

also contains an account of a new astronomical telescope with two convex

lenses. Towards the end of his life he wrote a small work on the gauging of

wine casks, which is regarded as one of the significant works in the prehistory

of the integral calculus. In lighter vein he also wrote a paper discussing

why snowflakes are hexagonal.

Unlike Kepler himself, Catharina did not like living in Prague. She

never felt comfortable in court circles. Moreover, she was often homesick

and became upset when they ran short of money. He began to search

Johannes Kepler (1571–1630) 13

for suitable employment in a place she would find more congenial. The

need became pressing in May 1611 when Rudolph was deposed and Prague

became a scene of bloodshed in the struggle for the kingdom. Moreover,

Kepler’s wife became seriously ill and their three children were stricken with

smallpox, from which his favourite son died. Throughout his life Kepler kept

trying to obtain a position in ProtestantWu¨ rttemberg, but without success,

and now any remaining hopes of this were finally dashed when the theologians

of Wu¨ rttemberg raised objections to his Calvinistic sympathies. He

declined the offer of a professorship at the University of Bologna. Instead

he decided to move to Linz, the chief city of Upper Austria, where he had

been offered the specially created post of provincial mathematicus. However,

before the move could take place his wife died from the typhus brought

to Prague by the troops. It was not until January 1612 that he was able to

leave for Linz; by then his appointment as imperial mathematicus had been

renewed, so he was able to hold this as well as his provincial post, which

was virtually a sinecure.

Soon after he arrived in Linz Kepler began to look for a new wife. In a

letter he listed in detail eleven possibilities, and explained how God led him

to choose the fifth, a woman who had evidently been considered beneath

him by his family and friends. She was Susanna Reuttinger, a twenty-fouryear-

old orphan; the marriage was far happier than the first, but, of their

seven children, five died in infancy or childhood, as had three of the five

children of his first marriage. Then his aged but meddlesome mother was

accused of and tried for witchcraft, and Kepler had to travel toWu¨ rttemberg

to arrange for her defence, which occupied much of his time and energy over

the following three years. She was imprisoned and threatened with torture

but in the end set free; she died shortly afterwards.

Kepler, a peaceful and deeply religious man, suffered greatly for the

sake of his conscience throughout his life, particularly in Linz. His long stay

there had started badly, for the local Lutheran pastor, who knew the opinion

of the Wu¨ rttemberg theologians, excluded him from holy communion

because of his Calvinistic tendencies. Kepler did not accept the exclusion

willingly and made repeated appeals to the Wu¨ rttemberg consistory, but

always in vain. While his co-religionists considered him a renegade, the

Catholics tried to win him to their side.

All these troubles notwithstanding, Kepler published two major

works during his fourteen years in Linz. The more important was his

Harmonicae mundi, a work that had occupied him on and off for many

years; this was published in 1618, with a dedication to King James the First

14 From Galileo to Daniel Bernoulli

of England. This has been described as a great cosmic vision woven out of

science, poetry, philosophy, theology and mysticism. Kepler believed that

the archetypal principles of the universe were based on geometry rather than

on number, and it is in this work that the regular polyhedra known as the

stellated dodecahedra make their debut. His other major work of this period

is his Epitome astronomiae Copernicanae, a textbook of the Keplerian

system. In the dedication he wrote ‘I like to be on the side of the majority’,

but in his Copernicanism and in his deep-felt religious convictions he rather

learned the role of being a member of a staunch, lonely minority. However,

it was Galileo, a far bolder polemicist, who became the persuasive purveyor

of the new cosmology.

When the counter-Reformation swept into Linz in 1625 an exception

was made so that he was not banished, but his library was temporarily

sealed and his children forced to attend Catholic services. By the summer

of 1626 Linz was blockaded and Kepler’s house, alongside the city wall, was

burnt down. As soon as the long siege had been lifted, Kepler petitioned the

emperor for permission to move to Ulm, where he knew that there were

printers who could undertake the composition of the Tabulae Rudolphinae.

Although he had worked in Linz longer than he had in any other place,

Kepler was not sorry to leave. He packed up his household effects, books,

manuscripts and printing equipment and travelled by boat up the Danube

to Regensburg. After settling his wife and children he continued by road to

Ulm to see the Tabulae Rudolphinae through the press. Even before that

task had been finished, Kepler began to search for a new base. England was

one possibility; in 1620 the English Ambassador Sir Henry Wootton had

called on him in Linz and invited him to England, but nothing came of

this. In fact Kepler never moved out of the region consisting of southern

Germany, Bohemia and adjacent Austria.

In the end, reluctant to lose the financial security provided by his

salaries as provincial and imperial mathematicus, Kepler went back to

Prague to apply to Rudolph’s successor for these appointments to be continued.

The newly crowned king received him graciously, promising a reward

for the dedication of the Tabulae Rudolphinae, but making it clear that the

astronomer needed to become a Catholic if he wanted to remain in the imperial

service. The imperial commander-in-chief, Albraecht von Wallenstein,

was more accommodating.Wallenstein, then at the height of his power, had

just been granted the duchy of Sagan in Silesia as a personal fief. Anxious

to raise its status, as well as to have close access to an astrologer, he

appointed Kepler as his personal mathematicus. Kepler objected that he was

Johannes Kepler (1571–1630) 15

unwilling to ‘let himself be used as an entertainer’ and would not compromise

his own scientific convictions to satisfy his astrologically minded

patron. However,Wallenstein, who had no real interest in science, compromised

by employing Kepler to calculate the precise positions of the planets

and then obtaining the predictions from less-inhibited astrologers.

Kepler collected his family at Regensburg, settled his affairs in Linz

and finally reached Sagan in July 1628. He found the inhabitants unfriendly

and the local dialect almost incomprehensible. Before long religious strife

broke out when, for political reasons, Wallenstein started to press Catholicism

on his subjects. Although Kepler was not personally affected, the

persecutions made it difficult to attract printers to work on the Tabulae

Rudolphinae. He secured an assistant by the name of Jacob Bartsch, a young

scholar who had studied astronomy and medicine at Strasbourg, who later

became his son-in-law. Kepler wrote another book, the Somnium, which

described an imaginary journey to the moon and used this to present an

ingenious polemic on behalf of the Copernican system. The idea of universal

gravitation, which ‘vexed and haunted his mind’, seems implicit in his

description of the journey.

In Sagan Kepler waited in vain for the payment of his claims for arrears

of salary, the responsibility for which had been transferred to Wallenstein.

When the latter lost his position as commander-in-chief Kepler returned to

Regensburg, presumably intending to consult the emperor and friends at the

imperial court about his future and to collect at least some of his arrears

of salary. However, a few days after arriving there Kepler became sick with

an acute fever; his condition steadily worsened, he became delirious and,

on November 15, 1630, he died. The symptoms are those of typhus, which

was prevalent during the Thirty YearsWar. He was buried in the Protestant

cemetery, soon to be completely destroyed in the conflict. His wife and

children were left almost destitute, but Jacob Bartsch helped them collect

the money owed to Kepler’s estate by the state treasury. A wealth of papers

left by the great astronomer passed through various hands; much has been

lost but the remainder is to be found in libraries in Austria, Germany and

elsewhere. The thousands of manuscript sheets left at his death went to his

son Ludwig, who promised publication but lacked both the time and the

knowledge for such an undertaking. A monumental Gesammelte Werke in

nineteen volumes has been published, as well as a great deal of secondary

literature.

Kepler’s scientific thought was characterized by his profound sense of

order and harmony, which was intimately linked with his theological view

16 From Galileo to Daniel Bernoulli

of God the creator. He saw in the visible universe the symbolic image of the

Trinity. Repeatedly he stated that geometry and quantity are co-eternal with

God and that mankind shared in them because man is created in the image

of God. From these principles flowed his ideas on the cosmic links between

man’s soul and the geometrical configurations of the planets. Today, when

physicists are said to be searching for a ‘theory of everything’ that would

allow them to ‘read the mind of God’, we may be reminded of Kepler’s

indefatigable search for the mathematical harmonies of the universe. Yet

contrasting with this mysticism was his insistence on physical causes.

Kepler never rid himself of a feeling of dependence; neither could he

exhibit the imperious self-assurance of a Brahe or a Galileo. Nevertheless,

his ready wit, modest demeanour and scrupulous honesty, as well as his

wealth of knowledge, won him many friends. Although Newton seemed

reluctant to acknowledge his influence in the Principia, that great work

was presented to the Royal Society of London as ‘a mathematical demonstration

of the Copernican hypothesis as proposed by Kepler’, and Halley, in

reviewing the Principia, wrote that Newton’s ‘first eleven propositions were

found to agree with the phenomena of the celestial motions as discovered

by the great sagacity and diligence of Kepler’. In one of Galileo’s letters to

Kepler he states ‘I thank you because you were the first one, and practically

the only one, to have complete faith in my assertions.’

Although Kepler today is remembered chiefly for his three laws

of planetary motion, these were but the elements in his much broader

search for cosmic harmonies and a celestial physics. With the exception

of Rheticus, he became the first enthusiastic Copernican after Copernicus

himself. Kepler has been described as an astronomer’s astronomer; he found

an astronomy whose clumsy geocentric or heliostatic planetary mechanisms

typically erred by several degrees and he left it with a unified and

physically motivated heliocentric system nearly a hundred times more accurate.

The writer Coleridge, in his Table Talk, gave it as his opinion that

Galileo was a great genius and so was Newton, but it would take two or

three Galileos and Newtons to make one Kepler. Few would agree with

this sweeping statement but nevertheless Kepler’s enquiring mind helped

to break the mould of mediaeval cosmology.

Christiaan Huygens (1629–1695)

Unlike his English counterpart Isaac Newton, Christiaan Huygens came of a

distinguished family. His paternal grandfather had been secretary toWilliam

the Silent during the eventful years after 1578, when he had accomplished

Christiaan Huygens (1629–1695) 17

his mission of establishing a free commonwealth in defiance of the most

powerful empire then existing. The last quarter of the sixteenth century

saw the independence of the seven northern provinces of the Netherlands

completed after an eighty-year struggle with Spain. The father of the scientist,

Constantin Huygens, showed ability in mathematics but his education

was directed towards a career as a courtier and diplomat. As secretary to

the Prince of Orange he did much to guide his country through difficult

times. A man of outstanding ability and brilliance, he became a close friend

of Ren´e Descartes; after their first meeting Descartes wrote of him ‘I could

not believe that a single mind could occupy itself with so many things and

acquit itself so well with all of them.’ Constantin Huygens was a poet,

student of natural philosophy and classical scholar, as well as courtier and

diplomat.

Constantin Huygens married his cousin, Susanna van Baerke, daughter

of a wealthy merchant of Amsterdam and by all accounts an intelligent

and cultivated woman. Christiaan, their second child, was born on April 14,

1629, only a few months before the death of Kepler. There were four other

children, of whom Constantin the younger, born the previous year, is the

only one that concerns us here. When their mother died in 1637, after only

ten years of married life, another cousin took care of the family, which

moved to a house near The Hague. The two eldest sons, who early showed

18 From Galileo to Daniel Bernoulli

brilliance, were taught at home by a private tutor until 1645. Their education

included singing, playing the lute and the composition of Latin verse. Like

Newton as a boy Christiaan loved drawing and the making of mechanical

models, on which he spent much labour and ingenuity. From the beginning,

however, he showed special promise of ability in geometry, whereas

his brother Constantin excelled in literary compositions. Christiaan was

rather delicate and by nature gentle, and his sensitivity seemed almost feminine

to his father. Descartes was much impressed by some early exercises

of Christiaan and saw that great things might be expected from this rather

serious boy with the pale face and the large dark eyes.

In 1645, when Christiaan was sixteen, both brothers entered the University

of Leyden, where they studied jurisprudence and mathematics. The

mathematics professor, a prot´eg´e of Descartes, regarded Christiaan as his

best pupil. In 1644 Descartes had published his Principia philosophiae, an

attempt to reduce all the changes of nature to mechanical processes. Later

Christiaan recalled that ‘it seemed to me when I first read this book that

everything in the world became clearer and I was sure that when I found

some difficulty it was my fault that I did not understand this thought. I was

then only fifteen or sixteen years old.’

In 1647, after almost two years at Leyden, Christiaan Huygens joined

his brother in studying law at the College of Orange at Breda. This college,

of which his father was curator and in which Descartes seems to have taken

a personal interest, achieved a temporary fame but did not survive into the

next century. After his studies there were over, Christiaan Huygens began

to visit some of the neighbouring countries, notably Denmark. He made

plans for a visit to Paris in the company of his father but France, following

the death of Louis XIII, was in a state of disorder and it was not until 1655

that he first went to the French capital. Before that he was able to establish

contact with some of the French scientists through correspondence with

P`ere Mersenne, another friend of his father’s. Although Mersenne died in

1648, his influence on the young Huygens was important.

Any ambition Huygens might have retained for a diplomatic career

was abandoned whenWilliam II died in 1650. Instead he found his metier in

scientific research. In the next sixteen years he proved himself to be as good

at it as anyone else at this time, with the possible exception of Newton. He

studied telescopes and microscopes and introduced improvements in their

design. His studies in mechanics touched on statics, hydrostatics, elastic

collisions, projectile motion, pendulum theory, gravitational theory and an

implicit concept of force, including centrifugal force. He pictured light as

Christiaan Huygens (1629–1695) 19

a train of wave fronts, transmitted through a medium consisting of elastic

particles. Fundamental research in pure and applied mathematics, optical

studies and the discovery of the large satellite Titan of Uranus all belong to

this period. Thanks to his success in designing a more powerful telescope

than anyone else had managed, he was able in 1655 to detect the rings of

Saturn for the first time.

From 1655, when he settled in Paris, Huygens moved in an elegant

and leisured society, occasionally visiting the salons. Thanks, no doubt, to

his father’s influence, he became a prot´eg´e of the powerful Jean-Baptiste

Colbert. He toured the chateaux of the Ile de France and of the Loire Valley

and accompanied his father on a brief visit to London. Constantin was well

known in England; he had studied at Oxford, played the lute at the court of

James the First and received an English knighthood. When he returned to

England later, Christiaan was able to build on these contacts. His long stay

in Paris was interrupted in 1664, when he went back to The Hague for two

years.

On his return to Paris in 1666, Huygens was elected to membership

of the Paris Academy, which had just been established officially, and for the

next seventeen years he made the French capital his home. At the same time,

however, he was developing his contacts in London, where the informal

society of men of science which had been meeting in Gresham College had

become recognized as the Royal Society. On his second visit to London

Huygens was very impressed by this lively new body and thought that what

it was doing surpassed anything happening in Paris. He arranged to be kept

informed about scientific work in England, especially the discoveries of

Newton, whose investigations in many respects ran parallel to his own.

Having dealt with the Fronde and established himself in power the

young Louis XIV declared war on the new Dutch Republic. Rather surprisingly,

Huygens remained in Paris while his homeland was in danger.

Accepted as the most distinguished of the academicians, he presided over

the Paris Academy until 1675, using his diplomatic skills to see the new

institution through its formative years. In research he became interested

in the problem of determining longitude at sea, so important for navigation.

He invented the pendulum clock, intended for use on board ship, but

this was not a success. He then developed the use of springs as regulators in

clocks. His research in this area was published in his celebrated Horologium

oscillatorium of 1673.

I digress at this point to say a few words about the mathematical

work of the polymath Gottfried Leibniz, since it was Huygens who was his

20 From Galileo to Daniel Bernoulli

mentor during the period when Leibniz invented the differential and integral

calculus. Leibniz started work on this about 1673, some years after Newton

but independently. Both worked out complete algorithms that, except in

their foundation, are substantially those in use today. Although he is not

usually regarded as a physicist, Leibniz made some notable contributions

to natural philosophy, but to go into these here would be too much of a

digression.

Huygens never enjoyed good health. From early youth he suffered

from some kind of disability, perhaps migraine, accompanied by severe

headaches. A serious illness in 1670 brought about complete prostration

and he clearly believed himself to be close to death. Whatever it was, it

lasted in acute form for several weeks and it was three months before he

was able to return to work. Early in 1676 there was a recurrence, and this

time he showed greater caution in meeting the danger. Life in Paris, he

decided, seemed to be bad for his health, so he returned to The Hague for

treatment. To his brother he confessed his doubts about whether he would

ever return to the French capital and, even when he had recovered a year

later, he procrastinated under the pretext of uncertain health, while continuing

his scientific work in The Hague. It was not until the middle of 1678

that he returned to Paris; before long he was taken ill again.

Recurrent ill-health no doubt accounts for the reduction in his mathematical

and scientific work after 1680. Early in 1681 he was taken ill again

but not until September was he able to return to The Hague, where he

slowly recovered. He had hopes of returning to Paris but, after his patron

Colbert died in 1683, Catholic intolerance in France was undoing much

that Colbert had been at pains to build. Huygens’ position at the academy

was undermined; his nationality and religion told against him. In 1687

his father died. His brother Constantin accompanied William of Orange to

England the next year, leaving Christiaan feeling alone. He made a short

visit to England himself in 1689, when he went to Cambridge to see

Newton and to lend his support to Newton’s bid to become Provost of King’s

College, but too little is known about this. The illness which had dogged

him throughout his life again recurred in a severe form and, in March 1695,

Huygens felt it necessary to summon his lawyer and make final corrections

to his will. The following month he became worse and, from then until July,

pain and sleeplessness spared him hardly at all; his days were filled with

deep despair. He thought he was being poisoned, kept hearing voices and

lived in fear of losing his reason. Weakened by suffering, he died on July 9.

Isaac Newton (1642–1726) 21

The professional and serious interests of Huygens are the ones which

are foremost in his correspondence. Nevertheless, it would be a mistake to

consider him as always having been nothing but a patient researcher. He was

a man of wide culture and acquaintance throughout Europe. Neither was he

averse to feminine society. Marianne Petit, daughter of one of Louis XIV’s

engineers, seems to have had an attraction for Huygens; their separation

was due to her withdrawal from society when she entered a religious order.

There were also some distant cousins he visited in Paris and there is no doubt

he felt considerable attraction for the eldest of these. The parallel between

Newton and Huygens in natural philosophy is striking. No other natural

philosopher of the seventeenth century even approached their level. In

matters relating to physics, their intellectual menus are strikingly similar.

Working within the same tradition, they dealt with the same problems in

many cases and pursued them to similar conclusions. Beyond mechanics,

there were also parallel investigations in optics. At nearly the same time and

stimulated by the same book, Robert Hooke’s Micrographia, they thought

of identical methods for measuring the thicknesses of thin coloured films.

In his own world of abstract thought he was incomparable, as Leibniz said,

his loss inestimable. Yet Huygens’ influence beyond his own century was

slight, whereas Newton’s was enormous. One of his limitations was that

he worked alone, with few disciples. Also, like Newton, he often hesitated

to publish, and, when the work finally saw print, others had covered the

same ground. More important, however, was his philosophical bias. He followed

Descartes in the belief that natural phenomena must have mechanistic

explanations. He dismissed Newton’s theory of universal gravitation

as absurd, because it was no more than mathematics and proposed no

mechanisms.

Isaac Newton (1642–1726)

Isaac Newton was born on Christmas Day 1642 in Woolsthorpe Manor, a

farmhouse near the Lincolnshire village of Colsterworth, sixty miles northwest

of Cambridge. The baby was premature and at first was not expected

to survive. His yeoman father, who had only recently married, had died

three months before the happy event, leaving his mother Hanna to run

the family farm. In 1645 when the boy was three his mother married the

elderly Reverend Barnabas Smith, with whom she went to live at his rectory

in nearby North Witham, leaving her son in the charge of his maternal

grandparents. As a boy Isaac Newton appears to have had little affection for

22 From Galileo to Daniel Bernoulli

his stepfather, his grandparents and their children. He grew up lonely and

loveless.

At the age of twelve, after early education at local schools, Newton

was sent to King’s School at Grantham. Since it was too far away for him

to live at home during school terms, he lodged with an apothecary named

Clark, who seems to have been very kind to him and, in particular, encouraged

him to make things with his hands. On the death of her second husband

in 1656, his mother returned to Woolsthorpe with the three children from

her second marriage. Two years later she took the fourteen-year-old Isaac

away from school to help her manage the farm. He proved a somewhat

incompetent farmer, his mind too much on other things. On the advice of

his mother’s brother he was sent back to King’s School to prepare for entry

to the University of Cambridge.

Again he lodged with the Clarks; their stepdaughter Catherine Storey

became an intimate friend. According to the antiquarian William Stukely,

who had a long conversation with her in old age, Isaac was ‘always a sober,

silent thinking lad, and was never known scarce to play with the boys

abroad, but would rather choose to be at home, even among the girls.’ While

he was preparing for Cambridge his childhood affection for Catherine deepened

and it seems they became engaged to be married. Stukeley continues

‘Sir Isaac and she being thus brought up together, ’tis said that he entertained

a passion for her, nor does she deny it; but her portion being not

Isaac Newton (1642–1726) 23

considerable, and he being a fellow of a college, it was incompatible with

his fortunes to marry; perhaps his studies too. ’Tis certain he always had

a great kindness for her. He visited her whenever in the country, in both

her husbands’ days, and gave at a time when it was useful to her, a sum of

money.’

Newton was admitted to Trinity College in 1661 at the age of

nineteen. He began as a subsizar and then sizar, which meant that he had

to perform menial duties for his seniors in return for free board and tuition,

although his mother, who had been left comfortably off as the heir of her

second husband, could have paid for her son’s expenses as a commoner.

Although he was studying hard, he was not following the syllabus. As a

result, when he tried for a scholarship in his second year, he failed the

examination in geometry.

Owing to an outbreak of the bubonic plague the Cambridge colleges

were suspended for the years 1665/6 and so the young man went home. It

was atWoolsthorpe that he conceived the theories which were to revolutionize

science. When he returned to the university in 1667 Newton’s abilities

were starting to be recognized. Trinity elected him to a minor fellowship,

against strong competition, and, after this had been converted into a major

fellowship the following year, he was entitled to reside in the college indefinitely.

He acquired a patron in Isaac Barrow, the Lucasian professor of mathematics,

who was later to become Master of Trinity, a Crown appointment.

To become known in Court circles, Barrow secured the position of Royal

Chaplain and vacated the Lucasian chair in Newton’s favour.

Newton’s first lecture as Lucasian professor took place at Trinity

College in January 1670. It was about his research on optics, material which

would find its way into his book Opticks of 1704, a much more accessible

work than the Principia of 1686. The audience was small, no-one came to

the second lecture, and he continued talking to an empty room throughout

almost every lecture he gave for the next seventeen years. After that he

gave up all pretence of teaching, which he never enjoyed. Only three students

ever came to him for tuition; they were intellectually undistinguished

and nothing is known about how they found him.

Newton’s early enthusiasm for making mechanical models had developed

into a passion for making scientific instruments, especially optical

instruments. The celebrated reflecting telescope was a notable example of

his extraordinary skill. It was this that first brought him to the attention

of the Royal Society. When they heard about the instrument the fellows of

the Royal Society asked to see it. Newton sent them an improved model,

24 From Galileo to Daniel Bernoulli

which was received with acclamation. When he followed it up with a paper

about his optical research he was elected to the society forthwith. His fame

quickly spread throughout Europe, but unfortunately the next few years

were marred by troublesome controversies over his optical discoveries, particularly

with Robert Hooke over priority of discovery and with Christiaan

Huygens over theory.

As a young man Newton was an orthodox member of the Anglican

church but during this period he had come to doubt the doctrine of the

Holy Trinity. For the rest of his life he firmly adhered to the Arian heresy,

in which Christ occupies an intermediate position between God and man

and, unlike the Father, has no foreknowledge of the future. Newton became

convinced that Trinitarianism was utterly false and spent much time and

effort studying the Scriptures and the history of the early Christian church.

Like many others at this time, he interpreted the Book of Revelation in a

way that identified the Whore of Babylon with the Church of Rome but as

an Arian he also regarded the Anglican church as heretical. This created

a problem over his tenure of the Lucasian chair. It was a statutory condition

that those elected to college fellowships should present themselves for

ordination after a certain number of years. This applied to Newton, but as

an Arian he no longer felt able to reaffirm his belief in the articles of the

Anglican church. He consulted Barrow, who was still Royal Chaplain, and

took his advice to seek a dispensation from the requirement directly from

the King. This was forthcoming, not just for Newton but for the Lucasian

professors in perpetuity.

It was in 1670, or thereabouts, that Newton first became interested

in alchemy, which began as an offshoot of chemical experiments but soon

developed into an obsession. When he retreated into his academic sanctuary

at the end of 1676 it was in order to pursue his alchemical studies. He was

in contact with a number of other enthusiasts and studied the literature

exhaustively. The practice of alchemy was by its very nature mysterious and

the mass of writings Newton left on the subject has left scholars perplexed.

Newton had not seen much of his mother since he left home. She

died at Stamford of a fever in June 1679 during which her son ‘sate up whole

nights with her, gave her all the physick himself, dressed all her blisters

with his own hands & made use of that manual dexterity for which he

was so remarkable to lessen the pain which always attends the dressing the

torturing remedy usually applied in that distemper with as much readiness

as he ever had employed it in the most delightful experiments.’ Newton

was her executor and heir; as a result he became a man of substance.

Isaac Newton (1642–1726) 25

In 1684 the astronomer Edmond Halley came to visit him at Cambridge,

and this marked a turning point in Newton’s scientific career.

Spurred on by Halley, he composed the Principia between the autumn

of 1684 and the spring of 1686. It was presented to the Royal Society in

June 1686 and published the following year under its full title Philosophiae

naturalis principia mathematicae. It is said he deliberately made it abstruse,

using mathematical arguments to put off the uninitiated. The treatise

brought Newton great fame in Britain and abroad. The great French scientist

Pierre-Simon Laplace wrote ‘the Principia is pre-eminent above any

other production of the human genius.’ The demand for his masterpiece

grew steadily as its importance became more widely understood.

The 1680s were a difficult time for Trinity College financially; the

magnificent new library, designed by Christopher Wren, was costing the

foundation more than it could easily afford, and fellows no longer received

their full dividend; moreover, the depredations of the CivilWar had reduced

the endowment income of colleges generally. Newton was of a seniority

to have influence in the college and to play an active part in university

affairs. He was one of eight college fellows who accompanied the vicechancellor

to London in 1687 to present the university’s case in connection

with the illegal encroachments by James II. There was an attempt to

have him appointed Provost (i.e. head) of King’s College, Cambridge. He

was elected as a member of parliament for the university; he seems to have

made no use of the position before giving it up at the end of the year,

but it left him dissatisfied with academic life. At Cambridge he became

friendly with the Whig politician Charles Montague, later Lord Halifax, and

through him Newton made repeated attempts to obtain a position in the

capital.

It was about this time that the young Swiss mathematician Fatio de

Duillier entered his life. Fatio seems to have won his way into Newton’s

affections like no-one else. Fatio was twenty-two years younger than

Newton and was the son of a wealthy Swiss landowner who wanted him

to study divinity, but his more intellectual mother insisted that instead,

or as well, he should study science in Paris. Although he was not without

talent, Fatio showed an early flair for self-promotion and, soon after arriving

in London in 1687, was elected to the Royal Society. He soon acquired

the nickname ‘the ape of Newton’. He was acquainted with many of the

continental scientists personally, notably Huygens. Although much of the

correspondence between Fatio and Newton has been lost, what survives

seems much more intimate than Newton’s other correspondence.

26 From Galileo to Daniel Bernoulli

The relationship came to a sudden end in June 1693, when Newton

experienced something in the nature of a nervous breakdown, with depression

and paranoia. The episode lasted three or four months; after it was over

he never resumed creative scientific work. The cause is unknown; one suggestion

is that it was due to metallic poisoning, particularly poisoning by

the mercury often used in alchemical experiments, but there are objections

to this. When Newton resumed his career it was in an entirely new role,

which involved a complete change in his mode of life. In 1696, through

Montague’s good offices, he was appointed a Warden of the Royal Mint in

the Tower of London. This office had previously been treated as little more

than a sinecure but Newton plunged himself into the work. Because the

coinage had been debased by counterfeiting and clipping, the government

decided to call in the old coins in exchange for new ones, which would be

more difficult to counterfeit and impossible to clip.

Under Newton the Mint operated with greater efficiency than ever

before and it was to be a long time before it did so again. It was one of his

duties to ensure that counterfeiters and other miscreants were prosecuted.

To obtain a conviction required witnesses and Newton put his energy into

the task of producing them. He had himself commissioned as justice of

the peace in the home counties and operated a network of paid informers.

All this kept him busy for the next few years, at the end of which he was

promoted to the lucrative office of Master of the Mint. He resigned his chair

and fellowship at Cambridge; for some years his professorial duties had been

performed by a deputy.

When Newton moved to London, after thirty-five years in Cambridge,

he settled in a modest Jacobean house in Jermyn Street, near Piccadilly. He

persuaded a seventeen-year-old niece of his named Catherine Barton to come

and preside over his household. A witty and charming girl, she soon became

very popular in London society, the toast of the Kit-Kat Club. Although

her relationship with Newton seems to have been platonic, it may have

been otherwise with his patron Lord Halifax, who in his will left her well

provided for.

For some years, despite living nearby, Newton had not attended meetings

of the Royal Society. This was partly because he would encounter the

curator Robert Hooke, one of his principal adversaries. In 1703, after Hooke’s

death, Newton was elected president, an office to which he was re-elected

annually for the rest of his life. The status of the society, which had been

declining, soon began to revive under his presidency. He was knighted in

1705, during a royal visit to Cambridge, for his services to science. However,

even when president, Newton did not find it easy to express fundamental

Isaac Newton (1642–1726) 27

convictions in public. He preferred silence to the risk of criticism in which

he might find himself made an object of ridicule. Even so, he could not escape

controversy and his bitter quarrels with Leibniz and others loom large in

scientific history. Notoriously they, or rather their respective supporters,

quarrelled over priority over the invention of the infinitesimal calculus.

Just when Newton developed his direct and inverse theory of fluxions it is

hard to say, but Leibniz started work on the differential and integral calculus

about 1673, some years after Newton but independently. The ideas

involved were foreshadowed in the work of various earlier mathematicians

but Newton and Leibniz can nevertheless be regarded as the founders of the

subject in a way that would not be reasonable with their precursors. Both

worked out complete algorithms, which, except in their foundations, are

substantially those used today. Although the notation used by Leibniz is

somewhat illogical, it has displaced that used by Newton almost entirely.

By this time Newton was a wealthy man, and if he lived parsimoniously

it was entirely his own wish, for he was a generous contributor to

deserving persons and other good causes. He was scrupulously exact and

regular in business matters and spent very little on himself, except that he

entertained as befitted his official standing. Towards the end his memory

was much decayed, although earlier it had been exceptional. His hearing

was good and some myopia in early manhood had corrected itself later,

as it so often does. Apart from the nervous breakdown, he enjoyed good

health until his eightieth year, when he began to suffer from gout and other

troubles and was often in great pain due to stones in the bladder. In 1709

he moved to Chelsea for a year, then to a house near Leicester Square until

1725. Then, at the age of eighty-three, he moved again to Kensington, at that

time in the countryside, because he was having some trouble breathing; he

was thinking of retiring to Grantham, near his birthplace. In February 1727

he presided for the last time at a meeting of the Royal Society, after which

he became very ill and died on March 20. Following a state funeral, he was

buried inWestminster Abbey, where his baroque monument lies in a prominent

position in the nave while clustered around his feet lie memorials to

other illustrious British scientists, such as Charles Darwin and James Clerk

Maxwell.

Since Newton died intestate, his valuable property was divided up

among surviving relatives according to the law. The bulk of his fortune

went to ‘an idle fellow who soon spent it in cocking, horse racing, drinking

and folly’. After passing through various hands, most of his surviving

papers ended up in Cambridge. Books entitled The Chronicles of the Ancient

Kingdoms Amended and Observations on the Prophecies of Daniel and the

28 From Galileo to Daniel Bernoulli

Apocalypse of St John, which appeared after his death, indicate the questions

on which he had spent so much of his time; no-one took these very

seriously, but, together with his alchemical investigations, they have earned

him the title of ‘the last of the magicians’.

Biographers of Newton are handicapped by the shortage of useful information

about his life before he moved to London, the most interesting period

from the scientific point of view. Of his contemporaries Humphrey Newton

of Grantham (no relation), who served as his assistant and amanuensis for

five years, recalled:

He always kept close to his studies, very rarely went a-visiting & had

as few visiters . . . I never knew him take any recreation or pastime,

either in riding out to take the air, a-walking, bowling or any other

exercise whatever, thinking all hours lost that were not spent in his

studies, to which he kept so close, that he seldom left his chamber,

unless at term time, when he read in the schools, as being Lucasian

professor . . . he very rarely went to dine in the hall unless upon some

public days, then, if he had not been minded, he would go very

carelessly, the shoes down at heels, stockings untied, surplice on, and

his head scarcely combed.

‘Newton would with great acuteness answer a question’, he added, ‘but

would very seldom start one’. During five years, he said he saw Newton

laugh only once. ‘He had loaned an acquaintance a copy of Euclid. The

acquaintance asked what use its study would be to him. Upon which Sir

Isaac was very merry.’ He also described how excited Newton became when

writing the Principia:

so intent, so serious upon his studies that he sat very sparingly, nay

oftentimes he forgot to eat at all, so that going into his chamber I have

found his mess untouched of which I have reminded him, he would

reply ‘Have I?’ and then making to the table would eat a bit or two

standing. At some seldom times when he designed to dine in the hall,

he would turn to the left hand and go out into the street, where

making a stop, when he found his mistake, would hastily turn back,

and then sometimes instead of going into the hall would return to his

chamber again . . . when he had sometimes taken a turn or two [in the

garden] he would make a sudden stand, turn himself about, run up the

stairs, like another Archimedes with an eureka!, fall to write on his

desk standing, without giving himself the leisure to draw a chair to sit

down in.

Isaac Newton (1642–1726) 29

These recollections were echoed by Stukeley:

As well as when he had been in the hall at dinner, he has quite

neglected to help himself, and the cloth has been taken away before he

has eaten anything. Sometimes on surplice days, he would go forward

to St Mary’s church, instead of college chapel, or perhaps go in his

surplice to dinner in hall. When he had friends to entertain at his

chamber, if he stept into his study for a bottle of wine, and a thought

came into his head, he would sit down to paper and forget his friends.

Newton was stocky in his youth, stout later on. In dress he was usually

untidy and slovenly. Among his other peculiarities was a compulsion

to make draft after draft of many of his papers, for example as many as

eighteen, differing only slightly from each other, for the first chapter of his

Chronology, and he even felt the need to copy routine documents relating to

the business of the Mint. There are a number of portraits, also a death mask.

Descriptions of his appearance by those who knew him at various periods

are not entirely in agreement. John Conduitt, who eventually succeeded

Newton at the Mint and married Catherine Barton, tells us that

[Newton] had a lively and piercing eye, a comely and gracious aspect,

with a fine head of hair as white as silver, without any baldness, and

when his peruke was off he was a venerable sight.

However, others said:

In the whole of his face and make, there was nothing of that

penetrating sagacity which appears in his compositions; he has

something rather languid in his look and manner, which did not raise

any great expectation in those who did not know him.

and

Sir Isaac was a man of no very promising aspect. He was a short

well-set man. He was full of thought and spoke very little in company,

so that his conversation was not agreeable.

Against this, Stukely said that

although he was of a very serious and composd frame of mind, yet I

have often seen him laugh, and that upon moderate occasions. He had

in his disposition a natural pleasantness of temper, very distant from

moroseness, attended neither with gayety nor levity. He usd a good

many sayings, bordering on joke and wit. In company he behavd very

30 From Galileo to Daniel Bernoulli

agreeably; courteous, affable, he was easily made to smile, if not to

laugh . . . he could be very agreeable in company, and even sometime

talkative.

The farm tenant of Woolsthorpe described Newton as a man of very few

words:

he would sometimes be silent and thoughtful for above a quarter of

an hour together, and all the while almost as if he was saying his

prayers; but that when he did speak, it was always very much to the

purpose.

To his successor in the Lucasian chair he was ‘of the most fearful, cautious

and suspicious temperament that I ever knew’.

Early attempts to collect more material about Newton’s life yielded

disappointing results. For example his first assistant John Wickins, who

shared rooms with him for sixteen years, added little of substance to what

was known from other sources; and it is the same with his niece Catherine

Barton, except that some information given by her husband John Conduitt

may have come from her. As a result biographers, while repeating the wellknown

anecdotes, have not succeeded in providing a satisfactory account of

his private life. The early biographies have a tendency to hagiography and

do not give a true picture. Scholars of today have concluded that Newton’s

side of the argument in the controversies in which he became involved was

not always as convincing as his supporters made out.

The mathematician Augustus De Morgan was one of the first to try

to penetrate more deeply:

[Newton] had not within himself the resource from whence to

inculcate high and true motives of action upon others. The fear of man

was before his eyes. All his errors are to be traced to a disposition

which seems to have been born with him.

More recently, Louis Trenchard More wrote

He was singularly unable to form intimate friendships. Morbidly

suspicious and secretive, he was subject to peevish outbreaks of

ill-temper, even towards those who were his best friends. On such

occasions he stooped to regrettable acts which involved him in a

succession of painful controversies that plagued his life, robbed him of

the just fruits of his work, and disheartened his sincere

admirers . . . The Gods had showered on him at birth extraordinary

Daniel Bernoulli (1700–1782) 31

gifts such as have been given to almost no other man, but some evil

fate cursed him with a suspicious and jealous temperament which

marred his life. This taint in his blood did not show itself in the form

of ordinary vanity but in an inordinate sensitiveness to any personal

criticism or to a reflection on his personal honour. In spite of his love

of meditation and of peace free of all distractions it involved him in

constant quarrels and altercations; and during a long and illustrious

life it raised an impenetrable barrier between him and other men. To

his friends he was never more than lukewarm and he kept them

constantly uneasy lest they had offended him; to his rivals he was, at

times, disingenuous, unjust and cruel.

Daniel Bernoulli (1700–1782)

The remarkable Bernoulli family, originally from Antwerp, left the Spanish

Netherlands in the late sixteenth century to escape the persecution

of Protestants and settled in Basel, where they married into the merchant

class. Generation after generation they produced remarkable mathematicians,

beginning with the brothers Jakob and Johann. It is Johann’s irascible

son, the polymath Daniel, who is profiled here, although we could wish

to know much more about him. He was arguably the ablest Bernoulli of

them all; he contributed ideas and insights that not only shaped eighteenthcentury

science but also presaged future discoveries. Like Newton, he was

32 From Galileo to Daniel Bernoulli

even more famous as a physicist than as a mathematician, but he flourished

at a time when the two subjects were closely inter-related.

Johann Bernoulli was professor of mathematics at the University of

Groningen, in the Netherlands; his wife Dorothea was the daughter of the

patrician Daniel Faulkner. Their second son Daniel, the subject of this profile,

was born on February 8, 1700. Five years later Johann was appointed to

replace his elder brother Jakob as professor of mathematics at the University

of Basel and so, with his family, he returned to the main base of the Bernoulli

clan. The brothers Jakob and Johann were involved in several quarrels. The

most notable of these started with misunderstandings on both sides, but

quickly exploded into a public dispute, in which each opponent challenged

the other, found mistakes in the work of the other and expressed his low

opinion of the work of the other, not only in private letters but also in print.

In 1699 both brothers were elected to the Paris Academy on condition that

they would cease their disputes.

The young Daniel was a precocious student who studied logic and philosophy

at the university, earning a master’s degree at the age of sixteen. At

the same time his father Johann and elder brother Nikolaus helped him to

learn some mathematics. However, as a career for his son Johann first tried

to interest him in commerce and then, when that was a failure, grudgingly

allowed him to study medicine, first in Basel, then in Heidelberg and then

in Strasbourg, before returning to Basel. Daniel Bernoulli graduated from

the University of Basel in 1721 by writing a dissertation on the mechanics

of respiration. Having tried without success to obtain a teaching position in

Switzerland (the final decision among qualified candidates was decided by

lot, and Daniel was unlucky), he followed in his brother’s footsteps by moving

to Venice. There he gained some experience of practical medicine and

was going on to continue his medical studies in Padua when he was taken

seriously ill. At the same time he was pursuing research in mathematics and

the result of this was his important Exercitationes quaedam mathematicae

(Mathematical Exercises), published in Venice in 1724. In this he discussed

a wide variety of scientific subjects, including probability and fluid dynamics.

This attracted a great deal of attention and on the strength of it he was

offered a teaching position at the St Petersburg Academy.

Prize competitions were an important feature of scientific life at least

until the end of the nineteenth century. Originally they were a way of seeking

solutions to specific problems. They usually emanated from the royal

academies, notably those in Berlin and Paris, and, although they provided

an opportunity for an unknown young researcher, it was quite normal for

Daniel Bernoulli (1700–1782) 33

the well-established to enter. In the case of the Paris Academy, for example,

prizes were awarded for memoirs addressing specific problems in the mathematical

and physical sciences. Among the rules of procedure, each entry

had to be under a pseudonym or motto, accompanied by a sealed envelope

similarly inscribed containing the name of the author, although this could

often be guessed by the judges. The Bernoullis were often successful in these

competitions.

In 1725 Daniel, who had returned to Basel, won the prize (later he

was to win nine more) and then took up his appointment in St Petersburg,

accompanied by his brother Nikolaus. Although he was officially a professor

of mathematics, he worked in many different fields. For example, his medical

publications include important papers on muscular contraction and the

optic nerve, and his writings on physics include a paper on oscillation. In

mathematics he was particularly interested in probability and statistics. He

corresponded with d’Alembert about the correct way to assess the value of

risky medical procedures for patients of various ages. He demonstrated the

importance of probability for economics, and its relevance to gambling.

Unfortunately the harsh climate of the Russian capital proved too

much for his brother, who died in 1726 of a ‘hectic fever’. However, the next

year Daniel’s young friend and compatriot Leonhard Euler came out to join

him in St Petersburg. Daniel Bernoulli provided Euler with accommodation,

and they regularly took meals together. The two men often worked together

during the next six years, Daniel’s most creative period. Daniel’s research

interests at this stage lay mainly in mechanics, physics and particularly

hydrodynamics. Although his work in St Petersburg was highly successful,

he began to look for an opportunity to return to Basel. The only vacancy

at the university was a chair in anatomy and botany. Although these were

not subjects he was much interested in, he took the position. Accompanied

by his shy younger brother, named Johann after their father, Daniel went to

Basel via Danzig and Hamburg, then across the Netherlands to Paris, where

he was given a particularly warm reception.

Daniel continued to win the prize competitions of the Paris Academy;

he won ten altogether, on subjects as various as astronomy, gravity, tides,

magnetism, ocean currents and the behaviour of ships at sea. In 1734, when

the subject was planetary orbits, father and son had separately entered their

work and when they were successful they were told that they could share

the prize, which was larger than usual because there had been no award the

previous time one was offered. As a result a bitter dispute arose between

them. In this case Johann had behaved badly, but he was often involved in

34 From Galileo to Daniel Bernoulli

priority disputes in which he had a valid case, particularly with his brother

Jakob. Several of the discoveries to which the name Bernoulli is attached

were Johann’s but it was Jakob who got the credit.

Daniel Bernoulli’s masterpiece, the seminal Hydrodynamica, sive de

viribus et motibus fluidorum commentarii (Hydrodynamics, or Commentaries

on the Forces and Motions of Fluids) was published in 1738, although

it was largely completed in St Petersburg. This confirmed his reputation as

one of the leading scientists of his time. Although he missed finding the

basic partial differential equations of hydrodynamics, the Hydrodynamica

contained other important advances. One is the principle, to which the

name of Bernoulli is attached, that the pressure of a fluid diminishes as its

velocity increases. This is fundamental to aerodynamics and much other

modern industrial design. Even more important is his explanation of the

mechanics of gases, which he regarded as composed of fast and randomly

moving particles. He established the theory underlying Boyle’s law, which

had been deduced experimentally, and realized that the pressure of a gas is

in direct proportion to its temperature. Altogether he may be said to have

laid the foundations of the modern kinetic theory of gases.

Unfortunately publication of the Hydrodynamica was delayed, leaving

his claim to priority open to attack, and the one to take advantage of

this was his own father, who rather resented his son’s success. They were

already on bad terms because father and son took different sides in the priority

dispute between the followers of Leibniz and Newton regarding which of

them invented the differential and integral calculus. Johann was an ardent

disciple of Leibniz while Daniel, who was more of a physicist, adhered to

the side of Newton. Johann attempted a blatant priority theft by publishing

a book on hydrodynamics in 1743 and dating it 1732. Daniel was understandably

upset and wrote to Euler ‘Of my entire Hydrodynamica not one

iota of which do I in fact owe to my father, I am all at once robbed completely

and lose thus in one moment the fruits of the work of ten years. All

propositions are taken from my Hydrodynamica, and then my father calls

his writings “Hydraulics, now for the first time disclosed, 1732”, since my

Hydrodynamica was printed only in 1738.’ The situation was not quite as

clear cut as Daniel claimed, but at any rate Johann Bernoulli’s deception

backfired. His reputation was so tarnished by the episode that he did not

even receive credit for the parts of the work which were original.

In 1737 Daniel Bernoulli had delivered a historic lecture about the

work done by the action of the heart. Six years later he was appointed professor

of physiology at Basel, a field he much preferred to botany. Finally, in

Daniel Bernoulli (1700–1782) 35

1760 he obtained the chair of natural philosophy, or mathematical physics,

which best matched his scientific interests. He applied himself to solving,

with the aid of the new analysis, difficult mechanical problems that had

defeated the more geometrical methods of Newton and Huygens. Although

it would be going too far to say that he enunciated for the first time the

principle of the conservation of energy, perhaps the most useful idea in all

of science, he came closer to this than did anyone else until the 1840s. It

was in the field of physics that he most brilliantly applied his mathematical

genius. He is regarded as one of the main pioneers of that branch of science

later known as mathematical physics.

Daniel Bernoulli also applied his mathematical insights to natural

phenomena. While studying the nature of sound, for example, he discovered

distinct mathematical regularities in the shape of sound waves and so

was able to calculate the natural frequencies of a variety of musical instruments.

His seminal work in the field of acoustics directly presaged such

great discoveries of nineteenth-century mathematics as the harmonic analysis

of Fourier. What he believed intuitively, namely that a sound can be

represented as a trigonometric function, Fourier was able to demonstrate

mathematically.

Daniel Bernoulli, who was an immensely popular lecturer, especially

on experimental physics, continued as professor of natural philosophy until

his retirement in 1776. Five years later he died in Basel on March 17, 1782, at

the age of eighty-two, and was buried in the Peterskirche. He regularly corresponded

with other leading scientists of the period. This was the age of the

scientific society and academy; Daniel Bernoulli was a member of many of

the most important, including those of Bologna (1724), St Petersburg (1730),

Berlin (1747), Paris (1748), London (1750), Bern (1762), Turin (1764), Zu¨ rich

(1764) and Mannheim (1767). In contrast to the other physicists profiled in

this chapter, we really know very little about his personal life; we do not

even know whether he was married. Of the sons of Johann, Daniel’s younger

brother was also an able mathematician, who was awarded four prizes by

the Paris Academy, but, although he lived to old age, a frail constitution

limited his scientific output. Historians of science are preparing an edition

of the Bernoulli papers and, when that is complete, we shall know much

more about the relationships of members of the family with each other and

with other scientists of the period.