5 From Kelvin to Boltzmann

Our next five remarkable physicists were born in the twenty-one years from 1824

to 1844. Two came from Scotland and one from each of Austria, England and

America.

William Thomson (Lord Kelvin of Largs) (1824–1907)

In 1894 William Thomson had held the chair of natural philosophy at

Glasgow University for fifty years; there was a great gathering of scientists

from all over the world to celebrate the occasion. Together with his friend

Helmholtz in Germany, he had been the foremost figure in transforming

the science of physics as it was known at that time. Three years later he

retired from the chair; the periodical Vanity Fair published a caricature of

him, with the following note:

He has been President of the Royal Society once, and of the Royal

Society of Edinburgh three times. He has been honoured by nine

universities – from Oxford to Bologna. He is the modest wearer of

German, Belgian, French and Italian orders, and he has been twice

married. He knows all there is to know about heat, all that is yet

known about magnetism, and all he can find out about electricity. He

is a very great, honest and humble scientist who has written much

and done more.

William Thomson, the future Lord Kelvin, was born on June 26, 1824

in a comfortable house on the outskirts of the Irish city of Belfast. He was

the fourth of seven children, four sons and three daughters. Their mother,

Margaret (n ´ee Gardner), came from a Scottish mercantile family. Their

father James Thomson, an Ulster Scot, was professor of mathematics at

the non-sectarian Belfast Academical Institution. Margaret Thomson died

in May 1830, shortly after giving birth to their youngest son Robert, so

the upbringing of the children devolved entirely on the father. In 1832 the

family, reduced to six children by the death of one in infancy, moved

to Glasgow, where James Thomson became professor of mathematics

at Glasgow College, the educational heart of the ancient University of

142 From Kelvin to Boltzmann

Glasgow, where he had earlier been a student. He was already known as

the author of several mathematical textbooks, the royalties from which

helped to supplement his meagre salary.

Initially William and his elder brother James were taught at home. In

1834 both boys began their formal education by matriculating at Glasgow,

where the academic environment was one characteristic of Scottish universities

at the time, which differed greatly from those of Oxford and

Cambridge. They were much more universities of the people, where untutored

boys were sent to train for the professions. In Scotland natural philosophy

was an essential part of an all-round course that began with philosophy

and ended with theology. Whereas at Cambridge there was not even a chair

of natural philosophy, at Glasgow there were professorships of astronomy

and chemistry as well as natural philosophy.

William Meikleham, then holder of the chair of natural philosophy,

had a great respect for the French approach to physical science, as exemplified

by Legendre, Lagrange and Laplace. Encouraged by Meikleham,William

Thomson read Laplace’s M´ecanique c´ eleste and Fourier’s Th´eorie analytique

de la chaleur in French during a family continental tour in 1839.

His brother James, who had a passionate interest in all things mechanical,

had decided to become an engineer. The third son John was embarking on

a career in medicine, but succumbed to the epidemic of typhus in 1847

which followed the famine in Ireland; the youngest brother Robert went

William Thomson (Lord Kelvin) (1824–1907) 143

into the insurance business and emigrated to Australia. Since William was

most attracted by mathematics, his father sent him to Cambridge.

Like Cavendish before him,William Thomson was admitted to Peterhouse,

where he was coached by the famous William Hopkins. Because of

the exaggerated importance attached to finishing in the first rank of the

Tripos examinations, Thomson’s studies at Cambridge did not influence

him as deeply as had those of his years at Glasgow. Much time and effort

was devoted to learning how to deal with the particular kinds of mathematical

problems set, which were only rarely related to any physical questions

that were not considered in Newton’s Principia.

His father was not surprised to find that, compared with Glasgow,

putting a young man through Cambridge was not cheap. He regularly

admonished his son not to be extravagant and to avoid gaining a reputation

for idleness and dissipation, advising him especially to avoid the rowdy

rowing men who would waste too much of his time. He was dismayed when

his high-spirited son, who was inclined to be impetuous, wrote that he had

bought a share in a small boat for himself, having been carried away by

the excitement of the boat races. Sculling, he told his father, was excellent

exercise and much more enjoyable than walking in the dull Cambridgeshire

countryside. Increasingly he participated fully in student life, winning trophies

for sculling, and became one of the most popular undergraduates of

his year.

When the time came for him to sit the Tripos examination in January

1845, Thomson came out second on the list. He was surprised not to be

senior Wrangler; no-one was in any doubt that he was the best mathematician

of his year. In the highly competitive examination for the Smith’s prize,

which followed, he came out first, having found the questions more to his

liking. He was elected a foundation fellow of Peterhouse and college lecturer

in mathematics later in the year, although still barely twenty-one.

He had done very well, but his future career was to be in Glasgow, not

Cambridge.

At Cambridge there was still little interest in the work of the French

analysts, but during his student years Thomson did not neglect to expand

his knowledge of French mathematical techniques and theories. Soon after

graduation, encouraged by his father, he travelled again to France. Quite by

chance he came across a reference to Green’s Essay, and was able to borrow

two copies just before he set off to spend the summer in Paris. He read it

on the journey and when he arrived showed it to Liouville, Sturmand other

French scientists. They were astonished to find that the unknown Green had

144 From Kelvin to Boltzmann

been at least twenty years ahead of anyone else. Thomson gave a copy of the

Essay to August Leopold Crelle for publication in his journal, and later it was

published again in a German translation. When Crelle asked Thomson to

provide a biographical introduction, he wrote to Caius for information, and

the college forwarded his letter to Sir Edward Bromhead. Sir Edward replied

and also contacted Tomlin. Without the letters they sent Thomson, we

would know even less about George Green. For the rest of his life Thomson

never failed to express his admiration for Green’s achievements.

Thomson’s studies in Paris were crucial for the subsequent development

of British physical science, but it was not so much the lectures as the

practice in new experimental work which he found so important later. He

said he was particularly indebted to his teacher Victor Regnault for ‘a faultless

technique, a love of precision in all things, and the highest virtue of an

experimenter – patience’. During this period he developed the technique of

electrical images, first read about Carnot’s theory of the motive power of

heat and formulated a methodology of scientific explanation that strongly

influenced Maxwell.

After his 1845 visit to Paris, Thomson returned to Scotland. The next

year, following the death of Meikleham, he was elected to the professorship

of natural philosophy at the University of Glasgow, the post he held for

the remaining fifty-three years of his life. The election was hotly contested,

but in the end he was selected unanimously. He was also elected a fellow

of the Royal Society of Edinburgh. In 1849 Thomson’s first great memoir,

A Mathematical Theory of Magnetism, was published, which led to his

election to the Royal Society of London. In 1851 a second great memoir

appeared, On the Dynamical Theory of Heat. In this work he postulated the

existence of a state of complete rest, which he called absolute zero, the base

for the temperature scale to which the name Kelvin is nowadays attached.

In these years he used to spend some time each summer in Cambridge, to

keep in touch with the scientists there and in London, and once or twice he

revisited Paris as well.

At that time neither in Scotland nor in England was there a research

laboratory in a university or anywhere else in which students could work.

Thomson, having enjoyed such facilities in Paris, was keen to establish

similar opportunities for his students, so he extracted a small sum from

the university for that purpose. It made possible the first teaching laboratory

in Britain, albeit of a modest sort. He was also greatly interested in

developing measuring instruments of high accuracy, and the facilities of his

new laboratory made that possible also. The new professor soon became

William Thomson (Lord Kelvin) (1824–1907) 145

popular through his radically new professionalism, marked by a clear

research orientation.

For an impression of Thomson in the lecture room we have these lines

of one of his students, written years afterwards: ‘Lord Kelvin [as Thomson

later became] possessed the gift of lucid exposition in ordinary language

remarkably free from technicalities. Occasionally he got out of range with

the majority of his class, but there was no obscurity in his statement, it was

simply beyond their grasp . . . he had no syllabus of lectures and used no

notes in lecturing. He had his subject clearly before him and dealt with it

in logical order. He was not dictating a manual of natural philosophy to his

students . . . he considered it unnecessary for him to teach what could be got

in an ordinary textbook and that his province was to supplement this.’ On

one occasion he described his method as follows: ‘the object of a university

is teaching, not testing . . . the object of the examination is to promote the

teaching. The examination should, in the first place, be daily. No professor

should meet his class without talking with them. He should talk to them

and they to him. The French call a lecture a conference, and I admire the

idea involved in the name. Every lecture should be a conference of teaching

and students.’

After his beloved father had died in an outbreak of cholera in 1849,

Thomson began actively seeking a wife. Disappointed in his overtures to

one young lady, he married, on the rebound, the highly cultured and intellectual

Margaret Crum in September 1852. She was three years younger than

he was and came from one of the newer commercial families of Glasgow,

with whom he had been friendly for many years. Unfortunately her health

declined rapidly following an exceptionally strenuous honeymoon tour

around the Mediterranean, and attempts at treatment were largely unsuccessful.

It is not known what was wrong with her, but, after prolonged

suffering and many setbacks, she died in June 1870, after seventeen years of

marriage. Another misfortune in this period was an accident when Thomson

was engaged in the Scottish sport of ‘curling’ on ice, in which he fractured

a thigh-bone; this continued to be troublesome for the rest of his life.

It was Thomson who drew the attention of the scientific world to the

theories of Sadi Carnot, the pioneer of thermodynamics, and his English

follower James Joule. For a number of years Thomson and Joule collaborated

on research in this area, and, in a posthumous tribute to Joule, Thomson said

that ‘the genius to plan, the courage to undertake, the marvellous ability

to execute and the keen perseverance to carry through to the end the great

series of experimental investigations by which Joule discovered and proved

146 From Kelvin to Boltzmann

the conservation of energy in electric, electromagnetic and electrochemical

actions, and in the friction and impact of solids, and measured accurately, by

means of the friction of fluids, the mechanical equivalent of heat, cannot be

generally and thoroughly understood at present. Indeed it is all the scientific

world can do just now in this subject to learn gradually the new knowledge

gained.’

The role that James Thomson played in the life of his younger brother

must not be underestimated. After working in industry for some years,

where he gained much valuable practical experience, James had settled in

Belfast and become professor of civil engineering at Queen’s College, until

in 1873 he moved to be professor of engineering in Glasgow. The Cambridge

mathematical physicist Sir Joseph Larmor referred to James as ‘the philosopher,

who plagued his pragmatic brother’ to obtain a comprehensive understanding

of the problems he dealt with. As Helmholtz explained in 1863,

‘James was a level-headed fellow, full of good ideas, but cares for nothing

except engineering, and talks about it ceaselessly all day and all night, so

that nothing can be got in when he is present. It is really comic to see how

the two brothers talk at one another, and neither listens, and each holds

forth about quite different matters. But the engineer is the more stubborn,

and generally gets through with his subject.’ At dinner parties where both

brothers were present, it was considered advisable to seat them as far apart

as possible.

Some of Thomson’s many scientific friends have already been mentioned,

but not all. One of his most important and long-standing friendships

was with the mathematical physicist George Stokes, later Sir George,

whose career was almost exclusively in Cambridge. From the time of their

first meeting in 1845 until the death of Stokes in 1903 they were in frequent

correspondence; Thomson seems to have consulted Stokes at every

opportunity. Another of Thomson’s disciples was Tait, who had become professor

of natural philosophy in Edinburgh; they collaborated on the classic

Treatise on Natural Philosophy, first published in 1867, which for many

years was the bible of theoretical physicists in Britain and other lands.

Tait, who thrived on controversy, was a prot´eg´e of the Irish mathematician

Sir William Rowan Hamilton and, after the latter’s death, took over the

mission of promoting the use of quaternions; Thomson firmly resisted his

attempts to use them in their joint work.

Telegraphy by land lines dates from about 1837; by 1850 there was a

successful submarine cable between England and France. However, it was

the Atlantic telegraph of 1866 which most caught the popular imagination,

William Thomson (Lord Kelvin) (1824–1907) 147

and Thomson played a leading part in that enterprise. His interest and reputation

brought him to the attention of a consortium of British industrialists

who, in the mid 1850s, proposed to lay a submarine telegraph cable

between Ireland and Newfoundland, to improve communication between

Europe and North America. Telegraphy was by then a well-developed and

extremely profitable business; the idea of laying such a cable was not new.

The undertaking provided perhaps the first instance of the complex interaction

between large-scale industrial enterprise and theoretical electricity.

Thomson was brought in early as a member of the board of directors

of the project and he played a central role in its execution. The directors

had entrusted the technical details of the project to an industrial electrician

named Whitehouse, and many of the difficulties which plagued it from the

outset resulted from Whitehouse’s insistence on employing his own system

of electric signalling. Thomson had developed a very sensitive apparatus, the

mirror galvanometer, to detect the minuscule currents transmitted through

miles of cable, but Whitehouse refused to use it. Thomson had asserted that

the length of the cable would, by a process of statical charging of its insulation,

substantially reduce the rate at which signals could be sent unless low

voltages were used, so low that only his galvanometer could detect the currents.

However, the Whitehouse–Thomson controversy stemmed primarily

from Whitehouse’s jealousy of Thomson’s reputation.

The first attempt to lay such a cable in 1857 ended when it snapped

and was lost. The second attempt, a year later, was successful, but the

high voltages required by the Whitehouse method reduced the ability of

the cable to transmit signals rapidly, just as Thomson had predicted. Whitehouse

privately recognized the inadequacy of his own instruments and surreptitiously

substituted Thomson’s galvanometer while claiming success

for his own methods. This deception was soon discovered, and the ensuing

controversy among Whitehouse, the board of directors and Thomson

combined theoretical science, professional vanity and financial ignominy.

A third cable was laid in 1865 and, with the use of Thomson’s instruments,

it proved capable of rapid sustained transmission. Thomson’s role as the

man who saved a substantial investment made him a hero to the British

financial community and to the Victorian public in general; indeed he was

knighted for it by Queen Victoria in 1866.

Sir William’s success with the Atlantic cable, and the close relation

thereby established between testing in the laboratory and application to the

electrical industry, opened the way for his ambitious marketing of scientific

knowledge. Through a carefully developed and cleverly exploited system

148 From Kelvin to Boltzmann

of patents and partnerships, his financial returns on his scientific capital

were such that he soon became a wealthy man. This kind of success was

deplored by other scientists, especially those of France and Germany, who

maintained an almost religious belief in the importance of keeping science

pure, uncontaminated by industrial applications.

Some of his most useful and profitable inventions were related to

navigation. One of the most successful was the patent magnetic compass,

of which no fewer than 10 000 were sold; this gradually superseded the

older type which was unreliable in ironclad ships. Sir William purchased

a schooner of 126 tons partly for his own pleasure but also so that he could

try out such inventions at sea. It also provided a way he could escape from

the pressures of his many different responsibilities. One cruise took him

to the island of Madeira, where he was entertained by the Blandy family

of wine shippers. It was then that he met Frances Anna Blandy, who was

about fourteen years younger, and they were married in 1874. Neither of his

marriages resulted in children.

Throughout the latter part of the nineteenth century the progressive

University of Glasgow was becoming increasingly cramped on its ancient

site among the slums in the High Street. Eventually enough money was

raised by public subscription, by government grant and by the philanthropy

of local industrialists to build a grand cathedral of learning on a new site,

which opened in 1870. It included a new physical laboratory, vastly superior

to the old one. Two years later Sir William was elected a life fellow of

Peterhouse, which had the result that he visited Cambridge more frequently

and was able to play a leading role in the efforts being made to reform the

university syllabus by introducing more natural philosophy. In 1876 and

again in 1900 the Mastership of Peterhouse became vacant and each time

he was asked whether he would be interested in the position. Each time he

declined decisively, as he did when the Cavendish chair became vacant in

1879. He was such a grand figure in Glasgow with his electrical engineering

business as well as his academic position that it is hardly surprising that

he did not wish to leave. In 1891 the students elected him Lord Rector of

the University of Glasgow, with which he was so closely associated, and in

1904 he was appointed Chancellor.

In 1876 the science journal Nature printed an appreciation of

Sir William’s achievements by Helmholtz, which concludes by saying that

‘British science may be congratulated on the fact that in Sir William

Thomson the most brilliant genius of the investigator is associated with

the most lovable qualities of the man. His single-minded enthusiasm for

William Thomson (Lord Kelvin) (1824–1907) 149

the promotion of knowledge, his wealth of kindliness for younger men and

fellow-workers, and his splendid modesty, are among the qualities for which

those who know him best admire him most.’

Although he was no longer young, Sir William still seemed to have

boundless energy and a list of all his varied activities would take up far more

space than is available here. However, one that should certainly be mentioned

is his first visit to America in 1884, to give a course of twenty lectures

on molecular dynamics at the new Johns Hopkins University in Baltimore.

The invitation originally came from the mathematician J.J. Sylvester, who

was then at Johns Hopkins but had moved to Oxford by the time the lectures

were delivered. The audience included many of the American scientists of

that time. Although on this occasion he was too busy with his other interests

to see much of the USA, he returned in 1897 for the meeting of the British

Association in Toronto and took the opportunity to visit the Canadian and

American West.

In 1892 Sir William was created Baron Kelvin of Largs in the County

of Ayr, the first ‘scientific’ peer of the realm (the Kelvin is the stream that

runs through the gardens of the university). This might not have happened,

however, had he not also shown his support for the Conservative Party, particularly

in relation to Irish questions. He always laid stress on his Ulster

Scottish background and thought of himself as more Irish than Scottish.

From his father he inherited the enlightened liberal tradition which owed

its origin to Ulster of the eighteenth century and which strove for the establishment

of a non-sectarian framework of government and institution, free

of party rivalry and based on merit alone.

In 1896, the jubilee year of his professorship, there were great celebrations

and he was decorated with the Grand Cross of the Royal Victorian

Order. In 1899, the year in which he retired from his chair, he became the

first foreigner to be decorated with the Grand Cross of the Legion of Honour.

Academic jubilees are regularly celebrated in continental Europe but less so

in Britain; Kelvin’s was a particularly splendid occasion, where messages of

congratulation reached him from all over the world, and it was remarked

that there was an unusual element of spontaneity to the celebrations.

In addition to Netherhall, his country seat near Largs, the Kelvins had

a London home at 15 Eaton Place, in Belgravia. In the House of Lords he made

some fourteen speeches, six of which related to maritime affairs. During the

same period he published almost 130 scientific papers, including six in the

year of his death and two published posthumously. His eldest brother James

died in 1892, at the age of seventy, and Elizabeth, the eldest sibling and last

150 From Kelvin to Boltzmann

surviving sister, also died in the same year. Thus he outlived all the other

members of his family and many of his closest scientific colleagues as well.

For a glimpse of the Kelvins at the turn of the century, an old friend of

theirs recalled the following: ‘The dear Kelvins arrived. He is a great source

of anxiety. He insists on doing everything but is not well and once or twice

in the last week he has turned faint at dinner. He did so last night but gulped

down some champagne&came around&went to a party in the evening. His

troubles are connected with digestion & Maimie is distracted and hoping

she is providing the right food. We love having them but shall be thankful

when they are safely away.’

In September 1907 Lady Kelvin suffered a major stroke. Her illness

rendered her aged husband anxious yet optimistic. Until then his own

health had been fairly robust, but at the end of November he too became

gravely ill: his doctor diagnosed the complaint as ‘a severe chill of the liver

(duodenal catarrh)’. The accompanying fever continued and Lord Kelvin died

in Netherhall on December 17, 1907, at the age of eighty-three. The funeral

took place at Westminster Abbey, two days before Christmas.

James Clerk Maxwell (1831–1879)

Clerk Maxwell is regarded generally as standing at the high-water mark of

classical physics. One of his greatest admirers was Albert Einstein, who

commented that ‘it was Maxwell who fully comprehended the significance

of the field concept; he made the fundamental discovery that the laws of

electrodynamics found their natural expression in the differential equations

for the electromagnetic fields. This led to the electromagnetic theory of

light, one of the greatest triumphs in the grand attempt to find a unity in

physics.’

James Clerk Maxwell was born on June 13, 1831 at 14 India Street,

Edinburgh, today the home of the International Centre for Mathematical

Sciences. John Clerk Maxwell, his father, was a land- owner of scientific

bent. He had built to his own design a modest house named Glenlair, on

an estate of 1500 acres near Dalbeattie in Galloway owned by the family.

He was an advocate (the Scottish equivalent of a barrister) although more

interested in technology than the law. Attending the meetings of the oldestablished

Royal Society of Edinburgh was one of his chief pleasures.

Another regular was John Cay, whose daughter Frances he married when

he was thirty-nine and she thirty-four. Apart from a daughter who died in

infancy, James was their only child. He was a delicate boy, like Helmholtz,

an odd and eccentric child of an unusually inquisitive nature. His mother

James Clerk Maxwell (1831–1879) 151

saw to his early education; after she died in 1839 her unmarried sister Jane

helped the boy’s father with his upbringing. At the age of eight he was

entrusted to a private tutor for a few years, until he was ready to begin

his formal education at the new Edinburgh Academy, which provided its

pupils with a good background in mathematics and some understanding of

physics, as well as the classical languages. When he left he was not only

top of the class in mathematics and English but very nearly so in Latin as

well. Although he had been shy as a young child, he lost the shyness at

school, where he came in for a lot of bullying, mainly because of his sensible

clothes, designed by his father, and his rustic Galloway accent, but

he also stuttered and, throughout his life, when ill at ease he could lapse

into ‘chaotic statements’. In class he began to enjoy classical literature and

mathematics and formed some enduring friendships, notably with Tait. As

soon as he was old enough, his father took him to the lectures at the Royal

Society of Edinburgh.

After six years at the academy the young man went on to the University

of Edinburgh, where he attended courses in natural philosophy and

mathematics; he was most impressive by Sir William Hamilton’s class in

logic. During the long summer vacations, when he was at Glenlair, he pursued

his own lines of investigation, feeling increasingly confident of his

152 From Kelvin to Boltzmann

mathematical and scientific powers. After three useful years at Edinburgh

the next step was to be Cambridge, although his father had misgivings about

this.

Following in the footsteps of Thomson a few years earlier, Maxwell

was admitted to Peterhouse, but, because there were rather too many able

students in his year, he was advised to migrate to Trinity, where the chances

of a fellowship after graduation would be better. There he was coached by

the legendary Hopkins, tutor of Cayley, Stokes and other well-known scientists.

In his obituary of Maxwell his friend Tait wrote that ‘He brought

to Cambridge in the autumn of 1850 a mass of knowledge which was really

immense for so young a man, but in a state of disorder appalling for his

methodical private tutor. Though that tutor was Hopkins the pupil to a

great extent took his own way; and it may safely be said that no high

wrangler ever entered the Senate-house more imperfectly trained to produce

“paying” work than did Clerk Maxwell.’ Hopkins described Maxwell

as ‘the most extraordinary man he had met within his whole range of experience;

it appeared impossible for him to think incorrectly on physical subjects.’

When the Tripos results were announced, Maxwell was surprised to

be listed only as second to the Canadian-born Edward Routh, but he came

equal first with Routh in the separate examination for the Smith’s prize. He

was already recognized as having genius. He was elected to the select essay

society called the Apostles, where he read an essay on the philosophy of science,

especially the history of the development of scientific ideas. Following

a period of ‘brain fever’, Maxwell became active in the Christian Socialist

movement, which tempered the Scottish Calvinism of his upbringing. At

this time Oxford University was wracked with religious controversy, but

Cambridge was less affected.

As an adult Maxwell was about five foot four in height, strong and

athletic. ‘He was possessed of dark eyes, jet black hair and beard, and in

complexion somewhat pale. His mirth was real, but never boisterous. In

disposition he was genial and patient, and he had great power of concentration

even amidst distractions. He had considerable knowledge and discrimination

in literature, he was a rapid reader, and he had a retentive memory.’

Another description of him at the age of eighteen is intriguing:

James Clerk Maxwell still occasioned some concern to the more

conventional amongst his friends by the originality and simplicity of

his ways. His replies in ordinary conversation were indirect and

enigmatical, often uttered with hesitation and in a monotonous key.

James Clerk Maxwell (1831–1879) 153

While extremely neat in person, he had a rooted objection to the

vanities of starch and gloves. He had a pious horror of destroying

anything – even a scrap of writing paper. He preferred travelling by the

third class in railway journeys, saying he liked a hard seat. When at

table he often seemed abstracted from what was going on . . .

Already Maxwell was acquainted personally with many of the British men of

science. Even before he went to Cambridge he had created a stir at a meeting

of the British Association in Edinburgh by an intervention in his broad

Galloway accent. Other men of science he met at Cambridge, especially

after he had become a fellow of Trinity in October 1855.

When he learned that the professor of natural philosophy at Aberdeen

had died, he decided to please his father, whose health was causing him

some anxiety, by applying for the post. Maxwell’s attachment to Glenlair,

and to the continuity of family tradition, was strong. In the winter of 1855/6

Maxwell returned to Scotland to be with his father and was at his side

in April 1856 when he suddenly died. Since it had been his father’s wish,

Maxwell accepted the Aberdeen chair when he was offered it. He had been

publishing work of steadily increasing quality ever since he was a schoolboy

and now was on the brink of his greatest achievement. At Cambridge

he had published his first paper on electromagnetism, the branch of science

in which he was to become supreme. He also took up the theory of gases,

another life-long interest. At Aberdeen he was responsible for the course on

natural philosophy given to students whose knowledge was fairly rudimentary.

There were fifteen lectures a week, plus demonstrations and examinations.

He introduced the idea of having students conduct experiments

themselves, rather than just observe them being done, and later introduced

the same practice in London and Cambridge. In addition he gave evening

lectures to artisans, perhaps reflecting the influence of Christian Socialism.

Maxwell had resigned his Trinity fellowship on appointment to the

Aberdeen chair but, as a Cambridge graduate, he could still compete for the

Adams prize. He proved to be the only candidate in a year when the subject

was the structure of the rings of the planet Saturn; he showed that they

could not be solid but must be made up of particles. Airy, the Astronomer

Royal, described his essay as ‘one of the most remarkable applications to

mechanical astronomy that has appeared for many years’. Principal Dewar of

Marischal College, one of the two that made up the university, occasionally

invited Maxwell to his house, where he met Dewar’s daughter Katherine,

who was seven years older than he was. They were married in June 1858.

154 From Kelvin to Boltzmann

She was not popular with his students or colleagues and became increasingly

neurotic as the years went on. She was jealous of his scientific friends to

such an extent that he could never invite them to his home.

At this period the existence of two separate colleges in Aberdeen,

Marischal and King’s, gave students a choice, since there were usually two

lecturers in each subject, but Maxwell and others were in favour of a merger.

When this was agreed in 1860 many redundancies were inevitable, and

Maxwell’s post was one of them. He was not much upset by this, because

there was a vacancy for a professor of natural philosophy in Edinburgh. Both

Maxwell and Tait applied for this. Tait had been runner-up for the Aberdeen

chair, but this time it was Tait who was successful, being considered a

much better teacher even if Maxwell was a far more powerful researcher.

However, it turned out that Scotland’s loss was England’s gain. The professorship

of natural philosophy at King’s College, London was also vacant

and Maxwell was appointed in the summer of 1860. Election to the Royal

Society of London soon followed.

King’s College had been founded in 1828 as an Anglican answer to University

College, itself a non-conformist answer to Oxford and Cambridge. In

London the Maxwells lived at number 8 (now 16) Palace Gardens Terrace, a

newly built house in Kensington. The attic of the house was converted into

a private laboratory. Maxwell taught and researched in the mornings as a

rule, the afternoons being devoted to riding in Hyde Park, and sometimes

carried out experiments at home in the evening; more usually he was out

giving lectures to artisans, as at Aberdeen, which he seems to have regarded

as more worthwhile than his college lectures. The ground floor was given

up to his brother-in-law, who was seriously ill; despite being very busy,

Maxwell helped his wife look after him.

Scientifically, Maxwell’s stay in London was the most fertile period

of his career. The precise formulation of the space-time laws for electromagnetic

fields was his greatest achievement. The differential equations

he formulated showed that the fields spread in the form of polarized waves

and with the speed of light. However, in addition to his work on electromagnetism,

he carried out both theoretical and experimental work on the viscosity

of gases, continued research into colour vision and took the world’s first

colour photograph. All this against a heavy teaching load. An added demand

on his time was membership of various national committees, such as the

British Association’s committee on electrical units; their recommendation

formed a basis for the electrical side of the international system adopted

in 1881.

James Clerk Maxwell (1831–1879) 155

While Maxwell was at King’s he got to know other men of science,

notably Faraday. They had begun to correspond while Maxwell was at Cambridge

but now Maxwell took the opportunity of meeting him personally

and attending his famous Friday evening lectures at the Royal Institution.

They got on well together. After one of the discourses, when Maxwell was

caught up in the crowd of people all pressing to get out, Faraday, appreciating

the similarity of the situation to that of molecules in gas, called to

him ‘Ho Maxwell, you cannot get out. If any man can find a way through a

crowd it should be you.’

After five years in London, Maxwell left to return to Glenlair. One

of the reasons was to enlarge the family seat, a project of his father’s that

the son regarded as a sacred trust; in any case he enjoyed being laird and

took his responsibilities very seriously. The other was to collect his scientific

thoughts together in his masterpiece, A Treatise on Electricity and

Magnetism, which finally appeared in 1873. During this period he also wrote

a textbook on heat, published in 1870, in which the famous Maxwell demon

makes his first appearance.

Maxwell was a wealthy man, who had no need to earn his living as

an academic. Of course he was isolated from the scientific community at

Glenlair, but kept in touch with his main associates by mail, particularly

with Stokes, Thomson and Tait; there was so much correspondence that the

post office provided him with a private mail box. Also the Maxwells usually

wintered in London, where he could participate in the scientific life of the

capital. At Cambridge, where he was several times an external examiner, he

had some success in extending the scope of the Tripos syllabus, for example

to include electricity and magnetism. In 1868 the position of Principal of

St Andrews University became vacant; Maxwell applied, but, despite strong

support from the faculty, he was not appointed, perhaps for political reasons;

the Principal is appointed by the Crown on the recommendation of the prime

minister of the day.

As we have seen, it was the universities of Scotland, rather than

England, that were in the vanguard of scientific education in the first half of

the nineteenth century; in physics, at least, Oxford and Cambridge were in

the doldrums. The situation began to improve after Royal Commissions to

enquire into the two ancient English universities were instituted in 1850. In

that year Oxford established the honours school in natural sciences. A year

later Cambridge followed suit with the natural-science Tripos; this excluded

physics, although the mathematical Tripos already included a good deal of

mathematical physics. When the enlightened Prince Albert was Chancellor

156 From Kelvin to Boltzmann

of the latter university, he wished to see some of the principles and practices

of the increasingly successful German universities adopted. Not a great deal

happened in this direction, but the need for reform was obvious. Although

the use of apparatus for class demonstrations of the principles of natural

philosophy, electricity and magnetism went back to the eighteenth century,

there was no professorship of experimental physics until 1870, when one

was established. For the initial appointment an attempt was made to interest

Thomson, as we know, and then Helmholtz. The electors then offered

the chair to Maxwell. His first impulse was also to say no, but in his letter

of refusal he asked a number of detailed questions about the position, and

the outcome was that he was elected on March 8, 1871.

In 1872 another Royal Commission, chaired by the eighth Duke of

Devonshire, William Cavendish, was charged with the task of looking into

the relation of the state with science, to assess whether more state support

might be needed. It uncovered some remarkable facts. At Oxford University

there were nine fellowships in natural science out of 165, at Cambridge

three out of 105. The duke, a second Wrangler and Smith’s prizeman, was

the Chancellor of Cambridge at the time. He decided to reform the university

off his own bat, and in 1874 the Cavendish laboratory was erected

through his munificence. The duke not only paid for the building, but also

for the apparatus needed to equip it initially. Since there had been no previous

physics laboratory in Cambridge, unlike in Oxford, Maxwell needed

to explain to the architect what was needed, on the basis of his own experience

and visits to laboratories elsewhere. The building served the needs

of Cambridge well for nearly a century. Not much else followed from the

report of the Devonshire Commission.

By this time Maxwell was an establishment figure, traditionalist and

conservative. Although he was an enthusiast for the popularization of science,

his lecturing style had never been good. In Cambridge the audiences

he drew were pitifully small, normally two or three, half a dozen at most.

He had always been interested in history of science, and had it in mind to

write a history of dynamics, in particular:

The cultivation and popularization of correct dynamical ideas since

the time of Galileo and Newton have effected an immense change

in the language and ideas of common life, but it is only within recent

times, and in consequence of the increasing importance of machinery,

that the ideas of force, energy and power have become accurately

distinguished from each other. Very few, however, even of scientific

men, are careful to observe these distinctions; hence we often hear of

J. Willard Gibbs (1839–1903) 157

the force of a cannon ball, when either its energy or its momentum is

meant, and the force of an electrified body when the quantity of its

electrification is meant.

Instead he settled down to editing the papers of Henry Cavendish, a

task he could easily have passed on to someone else. What he discovered,

in that mass of unpublished material, has already been described in the

profile of Cavendish. Tending to the needs of his invalid wife also took

up a lot of Maxwell’s time; at one point Maxwell did not sleep in bed for

three weeks, lecturing and running the laboratory by day, and sitting by

his wife all night. He transcribed all the Cavendish papers into legible form,

longhand, by himself, by candlelight in the long nights sitting at her bedside.

He had contracted smallpox at Glenlair soon after their marriage and often

asserted that her ministrations had saved his life. It seems strange that,

quite apart from R¨ ontgen, whose wife was tubercular, both Clerk Maxwell

and William Thomson (in the case of his first marriage), married women

who soon became chronic invalids, as did the mathematician Sir William

Rowan Hamilton.

Of his own collected papers, fifty-eight out of 101 were published

during this Cambridge period, but of these twelve are book reviews, six are

lectures, eight are articles he wrote for the Encyclopaedia Britannica, nine

are review papers and twenty-one are short (though often not unimportant)

notes. Only in 1878 does Maxwell seem to have returned to full production,

with the two powerful late papers on gas theory. However, from the

beginning of 1879 it had been observed that there had been ‘some failure of

the old superabundant energy’, and in the Easter term he had been unable

to lecture. During the summer he returned to Glenlair, improved in health

initially, but soon regressed. He knew that he had only months to live, and

returned to Cambridge in great pain to have Sir George Paget, his trusted

doctor, within call and ‘to be with friends’. While still in the prime of life,

he died on November 5, 1879, from abdominal cancer, like his mother, leaving

no descendants. He was buried in a cemetery near Glenlair next to the

graves of his parents and other Clerk Maxwells. A fire in 1929 left the house

which had meant so much to him in a ruinous condition.

J. Willard Gibbs (1839–1903)

In nineteenth-century America there was a growing interest in science, but

few scientists of distinction. Willard Gibbs, the outstanding American scientist

of his day, was little known to the general public in his own country.

He sprang from a family with long and distinguished academic, but not

158 From Kelvin to Boltzmann

scientific, connections. As one of them said, ‘Though but a few of them,

perhaps, could be termed of exceptional distinction, yet we find that for generations

back they were, without exception, men notable for their intellect,

education and integrity, who held positions of public responsibility; while

their wives, as far as the more limited records show, were often women of

an intellectual character.’

The subject of this profile was born in New Haven, Connecticut, on

February 11, 1839, the fourth child and only son of JosiahWillard Gibbs the

elder and of his wife Mary Anna (n ´ee Van Cleve). Of his three older sisters,

Anna, Eliza and Julia, only the first and third survived to maturity, while a

fourth sister Emily died when only twenty-three. Their father, born in 1790,

was a graduate of Yale College, the old university which gives the town of

New Haven its claim to fame, although previously the family had sent its

sons to Harvard. He was a good all-rounder and, although he was outstanding

in mathematics, he became professor of sacred literature at his alma mater,

where he taught philology. Their mother was a woman of unusual character

and attainments, who took a particular interest in ornithology.

The boy’s education began at home and continued at private schools

in New Haven, where he had a traditional classical education. As an

J. Willard Gibbs (1839–1903) 159

undergraduate at Yale from 1854 to 1858, Willard Gibbs excelled in mathematics

and Latin, gaining prizes in both subjects and winning scholarships.

After graduation he entered the Yale advanced programme in engineering

and earned the first American Ph.D. in that subject in 1863 with a thesis

On the Form of the Teeth of Wheels in Spur Gearing; he explained that

the subject reduces to an exercise in plane geometry. His mother died

in 1855, perhaps of tuberculosis, and his father in 1861. The son also

was suspected of being tubercular and suffered from astigmatism; probably

these were among the reasons why he did not volunteer to serve

in the armed forces in the American Civil War, which began just after

he had graduated. Instead he was appointed to a three-year tutorship at

his alma mater. At Yale, such tutors were expected to teach as required

any of the prescribed subjects of the first two years of the college course,

so Gibbs found himself teaching mainly Latin texts while continuing to

work on applied science. He patented ‘An Improved Railway Car Brake’,

a mechanism allowing American trains to dispense with the services of a

brakeman.

The close-knit family was now reduced to Willard and his two older

sisters Anna and Julia. The three of them set sail for Europe in 1866. They

went first to Paris, enjoying the life of the city, whileWillard Gibbs attended

lectures at the Sorbonne and the Coll`ege de France, mainly on mathematics

but also on physics, and studied the classic memoirs of the great French

scientists. His health was continuing to give cause for concern and so, on

medical advice, they spent the later part of the winter on the Mediterreanean,

at the end of which he was pronounced free of tuberculosis. They

then resumed their itinerary and travelled in leisurely fashion to Berlin,

where they spent two semesters. Here Gibbs’ younger sister Julia, who for

some years had been engaged to one of his classmates at Yale, married and

returned with her husband to New Haven, leaving the older sister Anna

to keep Willard company. Again he attended lectures on mathematics and

physics at the university and studied the German scientific literature. Since

Willard Gibbs senior was a German scholar, it may be assumed that his son

was sufficiently familiar with the language to derive real benefit from his

time in Germany, which was completed by two semesters in Heidelberg,

where he must have overlapped with the famous Russian woman mathematician

Sonya Kovalevskaya. In physics he would have had the opportunity

to hear Helmholtz and his distinguished colleagues Bunsen and

Kirchhoff. Although detailed information is lacking, these three years of

post-doctoral study in France and Germany seem to have been crucial to

160 From Kelvin to Boltzmann

his later development as a creative scientist. Britain was not included in

the itinerary. On his return to America in 1869 he brought back with him

a far more comprehensive overview, and a much deeper understanding, of

current research both in mathematics and in physics than he could have

easily obtained anywhere in the USA during this period.

At this time Yale was about to install its first new president in a

quarter-century and some of the senior professors wanted to redirect the

university onto a course more in keeping with the changing times. The

existing system was designed to train men of an active, extrovert disposition

for executive positions in politics, law, the church and commerce.

Religion and law were the chief objects of study.Willard Gibbs had absorbed

the distinctive spirit of the university without question. Together with his

sisters and brother-in-law, who was librarian of Yale, he settled down in the

home in which he had been brought up, with Julia taking the place of his

late mother. Yale appointed him professor of mathematical physics in the

graduate school in 1871. He was the first occupant of the chair and retained

it for the rest of his life. Professorial salaries at Yale were not meant to be

sufficient to live on, butWillard Gibbs was unusual in being paid nothing at

all; fortunately he had private means. In 1873 Bowdoin College, in Maine,

attempted to lure him away from Yale, but, although the only response of

the Yale Corporation was to pay him a small salary rather than none at all,

he chose not to leave New Haven: financial considerations did not weigh

heavily with him. In 1884 the new and innovative Johns Hopkins University

also attempted to attract him. Johns Hopkins was the first American university

to regard research as part of its mission, and, if he had moved to

Baltimore, Willard Gibbs would have been given the opportunity to create

the first research school of mathematical physics in the USA. However, he

still chose to remain at Yale.

Willard Gibbs had published nothing in mathematical physics at the

time he was appointed professor; in fact, his only real research had been

in engineering, not in physics at all. Nevertheless, by 1873 he had published

a contribution to the mathematical theory of thermodynamics in the

Transactions of the Connecticut Academy of Arts and Sciences. He went

on to revolutionize the study of physical chemistry in a two-part paper

‘On the Equilibrium of Heterogeneous Substances’ published in the same

journal between 1875 and 1878. Meanwhile he became an enthusiast for

Grassmann’s Ausdehnungslehre and Hamilton’s theory of quaternions: ‘if

Gibbs cannot be given credit for originality of methods yet he deserves praise

J. Willard Gibbs (1839–1903) 161

for the sensitivity of his judgement as to what deletions and alterations

should be made in the quaternionic system in order to make a viable

system’, wrote a colleague tactfully.

In his mature years Gibbs was a man of striking appearance:

A little over medium height, with a good figure, he carried himself

well and walked rather rapidly and with a purposeful stride. He was

always neatly dressed, usually wore a soft felt hat on the street, and

never exhibited any of the physical mannerisms or eccentricities

sometimes thought to be inseparable from genius. His hair and full

beard were grey and his complexion clear and ruddy – almost florid.

His eyes were blue and could twinkle amazingly on occasion. His

forehead was high, his nose well formed and of a good length, and his

mouth capable of a very sweet and intimate smile. In repose his

expression was rather grave and abstracted, but how it could light up

and become animated in greeting a friend or in pointing up a

humorous turn to the discussion! His countenance was very mobile

in conversation, every thought revealing itself in his changing

expression. His manner was cordial without being effusive and

conveyed clearly the innate simplicity and sincerity of his nature.

Being of a retiring disposition, Gibbs was not considered a good

teacher. His lecturing style, based on the logical exposition of abstract principles,

was clearly heavily influenced by the courses he had attended in

Germany, in contrast to the more-pragmatic British style based rather on

the development of skills relevant to the solution of practical problems.

Few students could understand what he was trying to convey. He worked

in almost total isolation, without the stimulus of colleagues or research

students, although he was in correspondence with men of science, particularly

in Britain. So far as is known, he never carried out any experimental

work. He was abnormally modest and reticent about his scientific

achievements, so his reputation is almost wholly due to his publications.

His great importance rests on his comprehensive application of mathematics

to chemical subjects, and, although some parts of his work were unwittingly

duplicated in Europe, his overall grasp of chemical thermodynamics,

a branch of science he can reasonably be said to have founded, was unrivalled

in his time. In statistical mechanics, his methods, which were more

general and more readily applicable than Boltzmann’s, came to dominate the

field.

162 From Kelvin to Boltzmann

The honours which came to Gibbs in later years were many and varied,

but his work was particularly appreciated in Britain. In 1885 he was elected

a corresponding member of the British Association, in 1891 an honorary

member of the Cambridge Philosophical Society and of the Royal Institution,

the next year an honorary member of the London Mathematical

Society. The Royal Society, of which he was a foreign associate, awarded him

the Copley and Rumford medals. Despite all these British honours, he never

set foot in Britain, although twice invited to address the British Association.

Again, although he was a corresponding member of the leading scientific

academies of continental Europe and the recipient of honorary degrees from

several European universities, he never returned to the continent. In his

homeland, amongst other honours he was elected to the National Academy

of Sciences at the early age of forty, although he seldom attended its meetings.

He was awarded the Rumford medal by the American Academy of Arts

and Sciences. He never became a member of the American Physical Society

and only joined the American Mathematical Society shortly before he died.

Except for a customary summer vacation in the Adirondacks, he never cared

to travel far from New Haven.

In 1898 Willard Gibbs lost his older sister Anna, the constant companion

of so many years. Towards the end of his life he was thinking about

the possibility of another visit to Europe, but nothing came of it. Early in

1903 he began to experience some health problems, which were not thought

to be serious, but suddenly in New Haven on April 28, 1903 he died aged

sixty-four. After his death not much was found in the way of unpublished

material, since it was his custom to work everything out in his head. He

did not read exhaustively in the literature of the subjects of his research.

He usually preferred to work out for himself the results obtained by others;

he said that he found that easier than trying to follow the reasoning of

someone else. It is significant in this connection that few succeeded in

learning about the discoveries he made from his own publications. His writings

demanded ‘extraordinary attentiveness and devotion’, it was said, his

mode of exposition was ‘abstract and often hard to understand’. Einstein

rated Gibbs’ book on statistical mechanics a masterpiece but added ‘it is

hard to read and the main points have to be read between the lines’. At a

different level the vector notation, so useful in physics, was invented by

Gibbs; although the advocates of quaternions stoutly defended Hamilton’s

theory, they gradually had to concede defeat. ‘If I have had any success in

mathematical physics’, he told one of his students, ‘it is, I think, because I

have been able to dodge mathematical difficulties.’

John William Strutt (Lord Rayleigh) (1842–1919) 163

John William Strutt (Lord Rayleigh) (1842–1919)

During the course of the nineteenth century the world of science became

increasingly institutionalized. Nevertheless, there were still first-class scientists

who, like Cavendish in the previous century, were not associated

with any particular institution, but preferred to work at home, at least for

the greater part of their career. Our next subject is one of the last of these.

He was born on November 12, 1842 as JohnWilliam Strutt, the eldest son of

the second Baron Rayleigh. The peerage, to which he later succeeded, was

of Terling Place, Witham, Essex; his birthplace was Langford Grove, near

Maldon, in the same neighbourhood. His immediate ancestors on his father’s

side were landed gentry with little or no interest in science. His mother

Clara Elizabeth la Touche (n ´ee Vicars) came from an Irish family with a distant

relationship to that of the scientist Robert Boyle. In his boyhood Strutt

displayed no unusual talent, just the normal boyish interest in the natural

world. Owing to occasional bouts of ill-health, his schooling consisted of

short periods at Eton and Harrow followed by four years at a small boarding

school near Torquay, where he showed no interest in classics but began to

develop decided competence in mathematics.

164 From Kelvin to Boltzmann

In 1861, being almost twenty, young Strutt went up to Cambridge and

entered Trinity College as a fellow-commoner like Thomas Young. Here he

became a pupil of Routh, the senior Wrangler of Maxwell’s year, who was

developing a reputation as an outstanding coach. Under Routh’s guidance

Strutt acquired the grasp of mathematics which stood him in good stead in

later years. He also benefited from the lectures of Stokes, the Lucasian professor

of mathematics, who was greatly interested in experimental physics

and performed many demonstrations in front of his classes using apparatus

of his own. In the mathematical Tripos of 1865 Strutt came out as senior

Wrangler and also came first in the Smith’s prize examination. By that time

he had clearly decided on a scientific career, though some members of his

family doubted the propriety of this in view of the social obligations inherent

in his eventual succession to his father’s title and position. However,

Strutt seems to have considered that such obligations should not be allowed

to interfere with scientific work.

In 1866 Strutt was elected a fellow of Trinity, thus further emphasizing

his scholarly leanings. By this time the traditional lengthy grand tour of

the continent by members of the aristocracy was going out of fashion. However,

with some friends he made a short visit to Italy, and the following

year he crossed the Atlantic, visiting Canada briefly but mainly the eastern

USA, then in the throes of reconstruction after the Civil War. Because

Strutt had a keen interest in politics, it was suggested that he might stand

for Parliament, as a representative of the University of Cambridge, but he

decided that, although he was in general a supporter of the Conservative

Party, he disagreed with its policy on certain questions; in any case, he

wanted to concentrate on a career in science. Immediately after his return

to England, he purchased an outfit of experimental equipment.

At Cambridge, because of the lack of a university physical laboratory,

students received little or no direct encouragement to embark on experimental

investigations for themselves. However, the young scientist’s first

serious research was experimental in character and the results were presented

at the Norwich meeting of the British Association in 1868. This

marked the beginning of a lifetime of research, stimulated by his own curiosity

and by early careful reading of the current scientific literature, which

provided many suggestions for independent investigations into the puzzles

and questions left by previous researchers. In those early days he was much

encouraged by correspondence with Maxwell, who was always eager to help

a youthful colleague.

John William Strutt (Lord Rayleigh) (1842–1919) 165

Strutt had become acquainted with Arthur Balfour, the future prime

minister, as a fellow student at Cambridge, and through him met his sister

Evelyn. They shared a common interest in music; he persuaded her to read

Helmholtz’s Theory of Sensations of Tone. They married in 1871; college

statutes meant that he had to vacate his fellowship on marriage. Not long

after this, a serious attack of rheumatic fever threatened for a time to cut

short his career and left him much weakened in health. On medical advice

he decided not to winter in England, so an expedition to Egypt was planned

as a recuperative measure. This took the form of a journey up the Nile by

houseboat as far as Nubia, during which he started work on his famous

textbook on the theory of sound. Shortly after returning to England in the

spring of 1873, Strutt succeeded to the title on the death of his father and

took up residence at the family seat of Terling; we should now refer to

him as Rayleigh, or the third Rayleigh, rather than Strutt. It was then that

he installed the laboratory where so much of his later experimental work

was done. The installation was by no means an elaborate one, and visitors

were inclined to be surprised that such obviously important results could be

obtained with what was considered even in his day to be rather crude equipment.

However, Rayleigh early manifested an economical turn of mind and

took real pleasure in making extensively improvised apparatus yield precise

results.

In 1873 Rayleigh was elected to the Royal Society. Six years later the

untimely death of Clerk Maxwell left the Cavendish professorship vacant.

Pressed by many scientific friends to let his name go forward for the post,

Rayleigh finally consented, being partly influenced by the loss of income

from the Terling estate due to the agricultural depression of the late 1870s.

It does not appear that he ever contemplated retaining the professorship for

an indefinite period and, indeed, he gave it up after five years. The teaching

duties of the Cavendish professor were not onerous; he was required to

be in residence for eighteen weeks of the academic year and to deliver at

least forty lectures during that period. The creation of a modern physical

research laboratory, he concluded, depends on a number of factors. Of course

a stimulating leader is essential. However, there have been many such who

failed to create schools because the other factors were not present; the leader

must be ‘one who is not only abounding in energy and ideas, but also one who

can without too great an effort throw himself into the difficulties of others.

This requires a peculiar kind of versatility not always easily combined with

great powers of concentration on any one line of thought. It is also necessary

166 From Kelvin to Boltzmann

to have a productive line of investigation opening up. Finally it is necessary

to have the right kind of pupils. They must be men of the not very common

kind of ability which makes a scientific investigator: they must not be too

young: and they must be provided with the means of subsistence while the

work goes on.’

Rayleigh embarked vigorously on a programme of developing elementary

laboratory instruction. It is difficult to appreciate what a task such a

programme involved; collegiate instruction in practical physics was almost

a new thing, and there was little to go on save the teacher’s imagination.

Under his direction laboratory courses were developed for large classes in

heat, electricity and magnetism, properties of matter, optics and acoustics.

This was pioneering work of a high order and a beneficial influence

on the teaching of physics throughout England and elsewhere. Previously

research had been carried on, by and large, outside the universities, which

thus remained quite out of touch with real progress in physics until well into

the second half of the nineteenth century. At the same time the publication

of his textbook on the Theory of Sound in 1877 also made an important

contribution to the teaching of theoretical physics; Helmholtz and Klein

had a very high opinion of it. It was a two-volume work; a third volume was

projected but never written. Because it was on the Nile that the book had

its genesis, the first part was written without access to a large library.

The stay in Cambridge was a period of broadening professional and

social relations. Through his relations by marriage, Rayleigh came into contact

with British politicians, especially those of the Conservative Party.

In particular, Lord Salisbury, several times prime minister, was a personal

friend. During the Cambridge period Rayleigh became increasingly involved

in the affairs of the British Association and was elected to preside over the

Montr´eal meeting of 1884, the first outside the United Kingdom. This meant

another visit to North America; he took advantage of this to spend two

months touring Canada and the USA, where he was hospitably entertained

by various American and Canadian physical scientists.

By this time Rayleigh’s financial situation had improved, so he did

not feel any further need for an income from his scientific work. Therefore,

immediately after the return from the USA, he resigned from his Cambridge

post and went back to Terling, which remained his scientific headquarters

for the rest of his life. Probably many contemporaries in the peerage as well

as some tenants on his estate thought his preference for scientific activities

rather peculiar, but Rayleigh went his own way with typical British imperturbability.

Terling is close enough to London to permit frequent visits to

John William Strutt (Lord Rayleigh) (1842–1919) 167

the metropolis, so Rayleigh could, without too much inconvenience, spend

time on committee work for the government or for bodies like the Royal

Society. Though he clearly loved his laboratory, he was no recluse and gave

freely of his time to endeavours for the advancement of science. He also

kept up a voluminous correspondence with scientific colleagues.

In the later stages of his career Rayleigh continued to take a lively

interest not only in the British Association but also in the Royal Society,

which he served from 1885 to 1896 as secretary and then from 1905 to 1908

as president. From 1882 to 1905 he held the chair of natural philosophy at the

Royal Institution, where he gave over 110 lectures in the afternoon series,

on a great variety of topics, and many of the evening lectures as well. In

1896, like Faraday before him, he was appointed scientific adviser to Trinity

House, involving numerous visits of inspection to lighthouses. Other public

services included serving as vice-chairman of the National Physical

Laboratory, as Lord Lieutenant of the County of Essex and as Chancellor

of the University of Cambridge, where he founded the prestigious Rayleigh

prize. Because of these commitments, the Rayleighs did not travel overseas

a great deal, but in 1897/8 they spent some time in India and in 1908 visited

East and South Africa.

Early in 1919 Rayleigh’s health began to give cause for concern, and

he died in his seventy-sixth year following a heart attack at Terling on

June 30, 1919. He was buried in the village churchyard; two years later

a memorial was erected to him in Westminster Abbey. Public recognition

of his achievements came to him in full measure. In 1904 he received the

Nobel prize in physics for his part in the discovery of the inert gas argon,

a previously unknown constituent of the atmosphere; he donated the cash

award which went with it to Cambridge University to improve the facilities

of the Cavendish Laboratory and the University Library. The next year

he was appointed to the Privy Council. In the course of his life Rayleigh

received numerous honorary degrees from universities at home and abroad

and many other distinctions. As one of the original recipients of the Order of

Merit in 1902, at the investiture he declared that ‘the only merit of which I

personally am conscious is that of having pleased myself by my studies, and

any results that may have been due to my researches are owing to the fact

that it has been a pleasure to me to become a physicist’. Meticulous experimental

work, characterized by extreme precision, was Rayleigh’s forte,

particularly during the Cambridge period when he helped to establish standard

electrical units for resistance, current and electromotive force. However,

he was also a very able applied mathematician, who invented what

168 From Kelvin to Boltzmann

became known as the WKB method of steepest descents. Like the majority

of British scientists of his period, the revolution in theoretical physics set

in motion by Planck was something he found difficult to accept.

Ludwig Boltzmann (1844–1906)

Although it would be going too far to say that there was a Viennese school of

physics, several remarkable physicists came from the imperial city. Under

the Habsburgs, Vienna was the hub of Mitteleuropa, but other cities such

as Breslau, Budapest, Cracow and Prague were also of major importance.

Cultural links with Germany were strong; knowledge of the German language

was taken for granted. There was a remarkable freedom of movement

between different universities in the area. Austrian universities followed

the German pattern, so that students had to face only one examination,

either for the certificate required for entry into one of the professions, or for

a doctorate. The first degree in physics was the doctorate of philosophy, for

which the candidate was required to present an original dissertation to the

faculty. Once the dissertation had been accepted the process was completed

by examinations called Rigorosa, one of which was a topic in philosophy,

as a concession to the title of the degree.

In 1837 Ludwig Georg Boltzmann, an Austrian tax official, married

Katharina Pauernfeind. He was a Viennese of Prussian ancestry; she was

the daughter of a businessman from a wealthy and old-established Salzburg

family. Their eldest son Ludwig Eduard was born in Vienna on February 20,

Ludwig Boltzmann (1844–1906) 169

1844. Two years later there was born a second son, who died in childhood,

and then a sister Hedwig. Their father was of the Protestant faith, but Ludwig

and Hedwig were brought up as Roman Catholics, like their mother. Young

Ludwig began his formal education when the family moved from Vienna

first to Wels and then to Linz, the chief city of Upper Austria, where he

began attending the local akademisches Gymnasium. He was an outstanding

scholar, showing particular aptitude in mathematics and science. Outside

school he took piano lessons from the composer Anton Bruckner and

throughout his life he maintained a strong interest in music. In appearance

he was short and stout, with curly hair and blue eyes; he suffered severely

from myopia.

In 1859 Ludwig Georg died from tuberculosis, a loss his son felt deeply.

In 1863 he enrolled at the ancient University of Vienna as a student in mathematics

and physics, receiving his doctorate three years later; the Austrian

Dr.Phil. was at about the level of a master’s degree; there was no equivalent

of a bachelor’s degree. The director of the institute of physics was the young

scientist Josef Stefan, later to become famous for the experimental discovery

of the relation between radiant heat and temperature. When Boltzmann

began research he particularly appreciated the close contact between Stefan

and his students: ‘When I deepened my contacts with Stefan, and I was still

a university student at the time, the first thing he did was to hand me a

copy of Maxwell’s papers and since at that time I did not understand a word

of English he also gave me an English grammar.’ Maxwell’s work did not

become generally known outside Britain until considerably later. In 1869

Boltzmann was awarded the venia legendi, the right to lecture, having been

appointed assistant professor the previous year. He began working at a small

laboratory in a house on Erdbergstrasse. The facilities were minimal, but

the physicists who worked there were full of ideas.

Two years later he was appointed to the chair of mathematical physics

at the University of Graz, which was rapidly rising in importance at that

time and soon ranked with the best in Central Europe. The director of

the institute of physics, August Toepler, had been appointed just before

Boltzmann and was working hard to develop the institute, with a new building,

new apparatus and much larger research funds. During the next few

years Boltzmann completed his theory of the statistical properties of gases,

in which the celebrated equation named after him makes its first appearance.

This was written up in a paper published in the Proceedings of the

Imperial Academy of Sciences of Vienna in 1872, under the title ‘Further

Researches on the Equilibrium of Gas Molecules’. In a relatively short time

170 From Kelvin to Boltzmann

his approach to kinetic theory became widely known, especially in Great

Britain. Although it was ridiculed by many at the time, his belief that thermodynamic

phenomena were the macroscopic reflection of atomic phenomena,

regulated by mechanical laws and the laws of probability, was his most

original contribution to science. Later his attempts to prove the second law

of thermodynamics were to be of decisive importance in the development

of statistical mechanics.

Thanks to funds obtained by Toepler, Boltzmann was able to make

short visits to other centres of research, notably Heidelberg and Berlin. At

the former university he worked with the chemist Bunsen and the mathematician

Ko¨ nigsberger, and at the latter with the physicists Kirchhoff and

Helmholtz. He was particularly impressed by the last of these, although

put off by the Prussian Geheimrat’s chilly manner. ‘Yesterday I spoke at the

Berlin Physical Society’, he wrote to his mother, ‘You can imagine how hard

I tried to do my best not to put our homeland in a bad light. Thus in the

previous days my head was full of integrals. Incidentally there was no need

for such an effort, because most of my listeners would not have understood

my talk anyway. However, Helmholtz was also present and an interesting

discussion developed between the two of us. Since you know how much

I like scientific discussions, you can imagine my happiness. Especially as

Helmholtz is not so accessible otherwise. Although he has always worked

in the laboratory nearby, I have not had a chance of talking much to him

before.’

In 1873 Boltzmann was offered a full professorship at his alma mater.

Although it was a chair in mathematics, not physics, it was considered

that ‘although his researches originated in physics they were also excellent

as mathematical works, containing solutions of very difficult problems

of analytical mechanics and especially of probability calculus.’ Boltzmann

accepted the offer despite the fact that in Graz the new institute of physics

had just been completed and transformed into an ideal centre for highquality

research in the most advanced physics of the time. The ambition

of every Austrian academic then, as now, was to become a professor at the

University of Vienna.

Before leaving Graz, Boltzmann had met his future wife, Henrietta

von Ailgentler, a young woman with long blonde hair and blue eyes, ten

years his junior. Having lost both her parents, she was making a living as

a schoolteacher. Boltzmann proposed marriage by letter, in which he said

‘Although rigorous frugality and care for his family are essential for a husband

whose only capital is his own work, it seems to me that permanent

Ludwig Boltzmann (1844–1906) 171

love cannot exist if [a wife] has no understanding and enthusiasm for her

husband’s efforts, and is just his maid and not the companion who struggles

alongside him.’ After this, she decided to study mathematics at the university.

Although she was allowed to attend lectures in the first semester,

at the start of the second the faculty passed a regulation to exclude women

students. Henrietta presented a petition to the Minister of Public Education,

a former colleague of her late father’s, who then exempted her from the regulation,

but the problem recurred, so to avoid it she replaced mathematics

in her studies by a course in cookery.

Boltzmann was not entirely happy in Vienna. For one thing he had

difficulty in finding an apartment to live in. For another he found that he

was expected to do a lot of administration. The main problem, however,

was caused by his teaching duties, which were those of a professor of mathematics,

not physics. So, when Toepler decided to leave Graz and move to

Dresden, Boltzmann applied for the post which he had relinquished. Ernst

Mach, then in Prague, also applied. Mach was a charming, unassuming man,

of whom the psychologist William James said that he had never had such

a strong impression of pure intellectual genius. Einstein admired Mach for

his independence, incorruptibility and ability to see the natural world as

through the eyes of a curious child. Like many other scientists of the time,

Mach believed that Newtonian physics needed revision. The Ministry of

Research and Education took a long time to decide between them, but in

the end Boltzmann was preferred. The young couple were then able to get

married and settle down to raise a family.

Of the fourteen years the Boltzmanns spent in Graz, at least the first

twelve were happy. They had two sons, Ludwig Hugo and Arthur, and two

daughters, Henrietta and Ida; a third daughter, Elsa, was born after the

family had left Graz. Professional recognition was not lacking. He was

elected to the Imperial Academy and received many honours from foreign

scientific academies. He was even offered noble rank, but declined, saying

‘Our middle-class name was good enough for my ancestors, and it will be for

my children and grandchildren as well.’ Occasionally he was invited to dine

with the Emperor Franz-Josef. Unfortunately he was a slow eater, whereas

the Emperor barely touched his food. Court etiquette did not allow guests to

continue after the Emperor had finished, so Boltzmann’s plate was removed

almost before he had started.

The nature-loving Boltzmann used to take long walks in the country,

during which he taught the children all about plants and butterflies. These

walks, coupled with ice-skating in winter, were his main form of exercise,

172 From Kelvin to Boltzmann

but he also enjoyed swimming and installed some gymnastic equipment in

his house for the family to use. He also bought a farmhouse near Oberkroisbach,

with a commanding view over a large part of Styria, and enjoyed country

life. He purchased a cow and consulted his colleague, the professor of

zoology, as to how to milk it. In Graz he entertained frequently, including

students among the guests. He was familiar with classical German literature

and liked to quote from Schiller and other standard authors. He played

the piano regularly, especially the works of Beethoven and Mozart. He also

played in chamber recitals and attended concerts and operas.

However, Boltzmann, lacking the stimulus he might have received

in one of the major centres of modern science, started to feel dissatisfied

and began to neglect his duties in the institute. On the experimental side,

he spent a considerable amount of effort on repeating the experiments of

Hertz and verifying Maxwell’s theory of the electromagnetic nature of light.

Scientific distinctions and awards kept arriving, but problems were on the

way as well.

In 1888 Boltzmann accepted the offer of the chair in Berlin made

vacant on the death of Kirchhoff, but, after Frau Helmholtz at dinner warned

him that he would not be happy in the Prussian capital because of his

informal style and well-known sense of humour, he created some annoyance

by withdrawing his acceptance. When, almost immediately afterwards,

he decided, for reasons that are unknown, that he must leave Graz anyway,

Munich seized the opportunity and appointed him to a newly created

chair in theoretical physics. At a farewell ceremony, his former colleagues

expressed the hope that he would return to Austria some day; the country

could not afford to lose one of its leading scientists. In Munich Boltzmann

was finally able to teach the subjects dearest to his heart. Although compared

with Vienna there was ‘wonderful equipment, but far fewer ideas’, he

added ‘we must not let the Austrian education ministry know that good

work can sometimes be done with inferior equipment’. Looking back to the

start of his career, he recalled that

Erdberg has remained through all my life a symbol of honest and

inspired experimental work. When I managed to bring some life into

the physics institute of Graz I called it jokingly ‘Little Erdberg’. By this

I did not mean that the space was small, it was probably twice as big

as Stefan’s institute; but I had not yet achieved the spirit of Erdberg.

Still, in Munich, when the young graduate students came and did not

know what to work on, I thought how different we were at Erdberg!

Ludwig Boltzmann (1844–1906) 173

Today there is nice experimental equipment, and people are looking

for ideas on how to use it. We always had enough ideas; our only worry

was the experimental apparatus.

Boltzmann spent four peaceful years in the Bavarian capital, during

which students came from all parts of Europe and even from as far away as

Japan to study under him. As well as lectures on physics, he gave lectures

on mathematics, especially the theory of numbers. He used to meet his

colleagues at the Hofbra¨uhaus to discuss academic questions over glasses of

beer. At this time university professorships in Bavaria were not pensionable.

Recalling the case of the blind Georg Simon Ohm, who died without a

pension in the most miserable circumstances, he started to worry about the

future of his family. His own sight started to deteriorate; he feared that he

was going blind. To spare his eyes, his wife Henrietta read the scientific

literature to him.

For some idea of his personality we can turn to some letters written

by a visiting Japanese physicist: ‘I think no-one can be as competent as he

[Boltzmann] is, except for Helmholtz. His lectures are extremely transparent;

he speaks lucidly, not like Helmholtz who speaks rather awkwardly.

But he is an odd little fellow and sometimes ends up doing unintelligent

things.’ Others recalled that ‘He never exhibited his superiority. Anybody

was free to put questions to him and even to criticize him. The discussion

would take place quietly and the student was treated as an equal. Only later

would the student realize how much he had learned from it.’ ‘He was not

upset even if a student disturbed him at home when he was working. The

great scientist remained available for hours, always keeping his patience and

good temper.’ As for his lectures: ‘He gave a course that lasted four years. It

included classical mechanics, hydrodynamics, elasticity theory, electrodynamics

and the kinetic theory of gases. He used to write the main equations

on a very large blackboard. By the side he had two smaller blackboards on

which he wrote the intermediate steps. Everything was written in a clear

and well-organized form. I frequently had the impression that one might

reconstruct the entire lecture from what was on the blackboards. After each

lecture it seemed to us as if we had been introduced to a new and wonderful

world, such was the enthusiasm that he put into what he taught.’

After a time Boltzmann began to feel a strong desire to return to

Vienna, and, when this became known, friends in Austria tried to find a

way to achieve this. A suitable opportunity arose when his former teacher

Stefan died in 1892, and there was a move to install Boltzmann as his

174 From Kelvin to Boltzmann

successor. Boltzmann was interested, but, when the conditions of his

appointment in Munich were improved, he felt that he ought to stay. Then

Vienna came back with another offer, including satisfactory pension rights.

For months he remained undecided, but he finally came down in favour of

Vienna and returned there in June 1894.

Boltzmann soon realized that moving back to Vienna was a mistake.

He made no secret of the fact that in Austria he found far fewer students

properly prepared for scientific work than in Germany. It was more like

secondary-school education, wasting his talents and aspirations, said his

wife. The pleasant social circle to which he had belonged eighteen years

before no longer existed. His university colleagues were not particularly welcoming.

The situation worsened when Mach, who rejected atomism, moved

to Vienna as well. For Boltzmann it was unbearable to have a ‘malevolent’

colleague who openly fought the very theory to which he had devoted his

entire professional life. ‘Boltzmann is not malicious but incredibly naive and

casual’, Mach wrote to a friend, ‘he simply does not know where to draw

the line. This applies to other things too, which are important to him.’

In 1900 Boltzmann decided to accept an appointment as professor of

theoretical physics at the University of Leipzig, where the physical chemist

Wilhelm Ostwald had built up a leading research centre. The Leipzig faculty

recommended Boltzmann as the ‘most important physicist in Germany and

beyond’. Unfortunately, the strain of reaching this decision led to another

nervous breakdown. Although Ostwald was a personal friend of Boltzmann,

he was also an ally of Mach and opposed Boltzmann’s theories violently,

so Boltzmann found himself in a worse situation than before. In addition

he felt homesick for Austria and made an attempt at suicide. He began

to negotiate for a return to Vienna, where the chair he had vacated had

not been filled and his adversary Mach had retired, after suffering a stroke.

However, the Minister for Research and Education did not find it easy to

explain Boltzmann’s personality problems to the Emperor Franz-Josef, or to

still rumours that he was mentally ill and would not be able to perform his

duties properly. Nevertheless, Franz-Josef agreed to his reappointment on

condition that Boltzmann gave his word of honour never to accept a position

outside the Empire again.

Fellow scientists from many lands contributed to a notable Festschrift

in honour of his sixtieth birthday; he had already received numerous academic

and scientific honours, including an honorary degree from Oxford.

Among the various countries Boltzmann visited for scientific purposes was

the USA. He first went there in 1899, accompanied by his wife, to lecture

Ludwig Boltzmann (1844–1906) 175

and receive an honorary degree from Clark University in Worcester,

Massachusetts. After a promising first decade, Clark was about to be eclipsed

by the even newer University of Chicago, but at the time Clark was an exciting

place to visit. They made a tour of the major cities of the eastern USA.

Five years later he was in St Louis for an International Congress, accompanied

by his son Arthur Ludwig, and the next year he gave a course at a

summer school held at the University of California at Berkeley. Unfortunately,

the audience found his English, of which he was very proud, almost

incomprehensible and were sorry he was not prepared to lecture in his native

language. He wrote an entertaining account of his experiences.

By all accounts, Boltzmann was an outstanding teacher on his home

ground. His mastery of his science and his love for it were combined with

a zest for lecturing and an attention to detail and procedure. He always lectured

completely without notes, but his blackboard technique was carefully

developed; the sequence of equations clearly inscribed on the board gave an

exact account of the structure of ideas he was expounding. The exposition

was not so formal and so highly polished as to smooth over the difficulties

or make the audience lose interest. Boltzmann never hesitated to point

out and correct his own errors; he welcomed questions and discussion, and

his lectures drew crowds of eager students. In 1902, for example, he began

his mechanics course by offering his students ‘everything I have: myself,

my entire way of thinking and feeling’ and asking the same of them: ‘strict

attention, iron discipline, tireless strength of mind’. One of those who heard

him was Lise Meitner, who recalled that

Boltzmann had no inhibitions whatsoever about showing his

enthusiasm when he spoke, and carried his listeners along naturally.

He was fond of introducing remarks of an entirely personal character

into his lectures . . . His relationship to students was very personal. He

not only saw to their knowledge of physics but tried to understand

their character. Formalities meant nothing to him, and he had no

reservations about expressing his feelings. The few students who took

part in the advanced seminar were invited to his house from time to

time. There he would play the piano for us – he was a very good

pianist – and tell us all sorts of personal experiences.

The return to Vienna was not without its problems. For example, he

had resigned from the Imperial Academy when he went to Munich but the

Emperor was against his immediate reappointment, so he had to wait to be

re-elected; Boltzmann thought this offensive. He led an active social life in

176 From Kelvin to Boltzmann

the city and yet was often still working in the early hours of the morning.

However, his health was becoming a major concern. His sight was steadily

deteriorating. He suffered from asthma, headaches and chest pains. He began

to worry that his wits and his memory would suddenly desert him in the

middle of a lecture. He suffered from the characteristic mood-swings of

manic-depression.

At least partly for health reasons, Boltzmann, with his wife and

youngest daughter, spent a few days at Duino, a village near Trieste, famous

for its castle perched on a rocky promontory of the Adriatic coast, having

the sea on one side and deep forests of cork trees on the other. It was there,

on September 5, 1906, at the age of sixty-two, that he took his own life. It

seems most likely that he hanged himself from a crossbar of the window

in his hotel room, while his wife and daughter were out swimming. The

following day he had been due to return to Vienna to start his lectures.

The dean of the faculty of philosophy at the university had written to the

Ministry the previous May that Boltzmann was suffering from a severe form

of neurasthenia and should abstain from any scientific activity. Boltzmann

had announced lectures for the summer semester but had to cancel them

because of his nervous condition. Mach wrote: ‘In informed circles one knew

that Boltzmann would most probably never be able to exercise his professorship

again. One spoke of how necessary it was to keep him under constant

medical surveillance, for he had already made earlier attempts at suicide.’