4 From Ohm to Helmholtz

Our next five remarkable physicists were born in the thirty-two years from 1789 to

1821. Two came from England, two from Germany and one from America.

Georg Ohm (1789–1854)

Two centuries ago the science and practice of electrical measurement hardly

existed. With a few exceptions, ill-defined expressions relating to quantity

and intensity retarded the progress of electrical investigations. Until well

into the nineteenth century there was no branch of physics in which there

were so many differences of opinion and uncertainties as in those related

to Galvanismus, and scarcely a physicist whose views did not differ from

those of every other upon important principles. Yet amidst this confusion

a discovery was made that was destined to create order out of chaos. This

discovery resulted from the experimental work of Georg Simon Ohm.

The future physicist, born on March 16, 1789 in the Bavarian university

town of Erlangen, was the eldest son of Johann Wolfgang Ohm, master

locksmith, and his wife Maria Elisabeth (n´ee Beck), daughter of a master

tailor. Of the Protestant couple’s seven children, only two others reached

maturity: Martin, born in 1792, and Elisabetha Barbara, born two years later.

Their mother died in 1799, when Georg was scarcely ten years old, but their

father lived until 1822. He was a remarkable autodidact, who gave his sons

a solid education in mathematics, physics, chemistry and philosophy, while

insisting that they also learn the locksmith’s craft. It is to the younger son

Martin that we owe an account of their early life in the (unpublished) autobiography

he left after his death in 1872.

According to this, the mathematical ability of Georg and Martin

was recognized at an early age by a professor of mathematics at the University

of Erlangen named Karl Christian von Langsdorff, who gave them

advice and encouragement. The gymnasium, which was associated with

the university, provided the usual classical instruction with just a little

history, geography and mathematics. After attending the school from 1800

to 1805, Georg Ohm went on to the university and studied mathematics,

physics and philosophy before lack of means and his self-sacrificing

108 From Ohm to Helmholtz

father’s disapproval at his supposed overindulgence in the pleasures of

dancing, billiards and ice-skating forced him to withdraw after just three

semesters.

So in 1806 the seventeen-year-old GeorgOhmbegan what proved to be

a long struggle to earn a living. He started teaching mathematics at a private

school in Gottstadt bei Neydau, a village in the Swiss Canton of Bern. In

his spare time he studied scientific works, such as those of Euler, Laplace

and Lacroix. He was hoping to be able to continue his university education

at Heidelberg but when he sought Langsdorff’s advice, it was that he would

do better to continue reading on his own. After two and a half years at the

school he obtained a position as private tutor in Neuchˆ atel for another two

years. During this period he had some contact with the nearby Pestalozzi

Institute, which had an important influence on his thinking about school

education, as we shall see.

In 1811, in accordance with his father’s wishes, Georg Ohm returned

to the University of Erlangen to obtain his degree. He subsequently taught

mathematics there as a Privatdozent for the next three semesters. Being

a fine draughtsman, he supplemented the meagre income this provided

by making architectural plans of the university hospital and library and

other works. Unfortunately there was little prospect of advancement at the

Georg Ohm (1789–1854) 109

university, and it was to be many years before he obtained a proper university

post. Soon lack of money obliged him to seek employment from the

Bavarian government as a schoolteacher; but the only post he could obtain

was one teaching mathematics and physics at the low-prestige and poorly

attended Realschule in Bamberg, where he worked with great dissatisfaction

until the school’s dissolution in 1816. The next year he was assigned,

in the capacity of auxiliary instructor, to teach a section of mathematics at

the overcrowded Bamberg Oberprim¨arschule. Meanwhile he wrote an elementary

textbook of geometry, dedicated it to his father and published it

in 1817. It was not a success.

Georg Ohm always lived simply. He was a man of marked energy, of

middle height, compactly built, sturdy and strong, what Germans describe

as the Martin Luther type of physiognomy. His eyes were large and penetrating;

his mouth revealed wit, satire and good humour. In diction and

phrase he excelled; moreover, his voice was full, and far into his life it

retained its attractive quality. He was a good, conscientious teacher, but

the conditions under which he worked were unfavourable. For example, the

Bamberg students had benches to sit on, but no desks at which to write.

Their mathematical knowledge at entry was so slight that physics to them

was at first unintelligible. He had progressive ideas about the role of mathematics

in education. The student, he believed, should learn mathematics as

if it were a free product of his own mind, not as a finished product imposed

from without. Ideally, by fostering the idea that the highest life is devoted

to pure knowledge, education should create a self-reliance and self-respect

capable of withstanding all vicissitudes. These views reflected not only his

own early education but also the years of isolation in Switzerland and of

personal and intellectual deprivation in Bamberg.

In 1817, the year his geometry textbook appeared, Georg Ohm was

appointed to the position of Oberlehrer of mathematics and physics at the

recently reformed Jesuit gymnasium in Cologne. He found there a library

and facilities for experimental work. Equally importantly he found congenial

colleagues who were enthusiastic about learning and teaching. Encouraged

by this, Ohm was able to combine research in the well-equipped

laboratory with his duties as a teacher; his students found him inspiring.

He prepared himself by studying the French classics – at first Lagrange,

Legendre, Biot and Poisson, later Fourier and Fresnel. However, it was

Oersted’s discovery of electromagnetism in 1820 that led him towards experimental

work in electricity and magnetism, particularly the elucidation of

the galvanic circuit.

110 From Ohm to Helmholtz

Meanwhile Georg Ohm’s younger brother Martin was getting on well.

He too had spent some years as a schoolteacher, in the course of which he

married a Swiss lady. He had written a textbook on number theory and,

perhaps as a result of this, had secured the position of Privatdozent at Berlin

University in 1821, which he combined with some teaching at the prestigious

Friedrich Wilhelm Gymnasium. In Berlin he made a good impression

on some of the influential members of the Academy of Sciences, which

led to his appointment as associate professor at the university in 1824, followed

fifteen years later by promotion to full professor. By contrast, his

brother Georg was overburdened with teaching and had become convinced

that his life had run into a dead end, that he must extricate himself from

what had become a stultifying situation in Cologne. Fearing that otherwise

he would never marry, he was determined to prove himself to the world

and to have something solid to support his efforts to obtain a position in

a more stimulating environment. He decided that he must devote himself

full-time to research and persuaded the authorities to grant him leave of

absence at half-pay for a whole year to pursue it in Berlin, alongside his more

successful brother Martin. The outcome was his masterpiece, the treatise

Die galvanische Kette, mathematisch bearbeitet, known in English as The

Galvanic Circuit, which appeared in 1827. This describes how resistance,

strength of current and potential difference are related. Among other results

this contains the fundamental law which bears his name.

Georg Ohm structured his theories in conscious imitation of Fourier’s

Th´eorie analytique de chaleur of 1822, a fact that may have led him to deemphasize

its experimental side in favour of an abstract deductive rigour, in

striking contrast to the inductivist tone of his earlier writings. Although he

did not spell out how, he wished the analogy between electricity and heat

to be taken seriously, not as something coincidental but as revealing some

underlying relationship. While Ohm’s law was independently confirmed by

other scientists, his theories came under attack, mainly because they were

based on experiment and observation rather than philosophical speculation

in the spirit of Hegel, whose romantic ideas were much in vogue at the time.

The criticism to which he was subjected demoralized Ohm, who resigned

from his position in Cologne in order to remain in Berlin with his brother.

For the next six years he was without a regular appointment, earning

a pittance by teaching cadets at the institution which later became the

Military Academy. A university post remained his goal, but in Prussia

the higher academic doors were closed to him. In influential quarters his

theories were rejected, if they were understood at all. Moreover, his brother

Georg Ohm (1789–1854) 111

Martin, with whom he was living, had acquired the reputation of being

a dangerous revolutionary. So in 1833 Georg decided to return to Bavaria,

hoping for a position at the University of Munich. In this he was unsuccessful;

instead, he was appointed professor of physics at the Polytechnic

Institute in Nuremberg, where he remained for the next fifteen years. Unfortunately,

apart from the title of professor, the position was no improvement

over the one he had held in Cologne.

After the publication of Die galvanische Kette, Georg Ohm turned

away from electrical research and directed his attention towards molecular

physics. His aim was to investigate, with the aid of analytical mechanics, the

form, magnitude and mode of operation of atoms, but he never had enough

free time to undertake such an ambitious project. Nevertheless, he continued

scientific research in other areas, notably he anticipated Helmholtz

when he discovered in 1843 that the human ear recognizes only sinusoidal

waves as pure tones, automatically performing an analysis of any periodic

sound into its component tones. Die galvanische Kette was translated into

English in 1841, fourteen years after its original publication, into Italian in

1847 and into French in 1860, although parts of the book were translated

earlier.

Increasingly, however, Georg Ohm was given other responsibilities,

in addition to his teaching duties, and these effectively put an end to his

researches into molecular physics. For some years he was Rector of the

Polytechnic Institute, while he also served as Inspector of Scientific Education

for the Bavarian State. It was not until 1849 that he achieved his

ambition of a senior post at the University of Munich, initially as associate

professor, then as full professor three years later. He was also given a seat

in the Senate and made curator of the mathematical–physical collection of

the Bavarian Academy. His last important piece of research was in 1852–3,

when he investigated interference phenomena in uni-axial crystals. By this

time, however, he was over sixty and almost blind, although unable to

retire because in Bavaria there were no pensions for university professors.

Following a stroke he died in Munich on July 6, 1854, having given what

proved to be his last lecture the previous day, and was buried in the Sudliche

Friedhof cemetery.

Georg Ohm had to wait a long time before his scientific work was

properly appreciated in his homeland, and for some years it remained largely

unknown anywhere else. However, by the early 1830s it was beginning to

be used by at least the younger German physicists working in electrical

science. British and French physicists seem not to have become aware of its

112 From Ohm to Helmholtz

profound implications until the late 1830s, but the situation improved when

the Royal Society of London awarded him its prestigious Copley medal,

particularly referring to his research on the conductivity of metals and on

galvanometers. It was acknowledged that it would have been of great value

to British investigators if they had known of his work earlier. Specifically,

Faraday, whose profile follows, was referring to Georg when he wrote in 1830

that ‘Not understanding German, it is with extreme regret I confess I have

not access and cannot do justice to the many valuable papers in experimental

electricity published in that language.’ Even ten years later the Manchester

physicist James Joule announced the law we know as Ohm’s law as if it were

a new discovery in a short paper submitted to the Royal Society.

As a Copley medallist and foreign member of the Royal Society, a

corresponding member of the Berlin and Turin Academies, a full member of

the Bavarian Academy and Knight of the Order of St Michael, Ohm was not

lacking in honours. Although at times he was miserably poor, it was said

that he displayed no bitterness as to his lot. Germany had been destabilized

by the Napoleonic wars at a crucial stage in his career, and, although Ohm

was not involved in the fighting, it was a miserable period for civilians as

well as soldiers. There can be little doubt that he could have contributed far

more to science if he had had better opportunity to do so. The Polytechnic

Institute in Nuremberg where he spent the major part of his career is now

the Ohm Institute; in front of it is a statue of Georg Ohm by Wilhelm von

Ru¨ mann, which was unveiled in 1895.

Michael Faraday (1791–1867)

James, the father of Michael Faraday, was the blacksmith of Outhgill, a

village near Kirkby Stephen in Westmorland. In 1786 he married Margaret

Hastwell, a farmer’s daughter, and soon afterwards they moved south and

settled in Newington Butts, south of the Thames near London Bridge. The

future scientist was born there on September 22, 1791, the third of four children,

of whom his sister Elizabeth and brother Robert were a few years older

and his sister Margaret a few years younger. The letters of Faraday’s parents

display intelligence and great religious earnestness. The father died in 1810

after years of poor health, leaving his impoverished widow to support herself

and the children by taking in lodgers. Her influence on her son Michael

was profound; she lived until 1838, by which time he had been recognized

as the greatest experimental physicist in the world.

From Newington the Faraday family moved house several times, ending

up near Manchester Square, on what was then the western fringe of

Michael Faraday (1791–1867) 113

London. Up to the age of thirteen Michael’s education ‘consisted of little

more than the rudiments of reading, writing and arithmetic at a common

day school’, he recalled, ‘My hours out of school were passed at home and

in the streets.’ In the same area there was a bookbinder and stationer’s shop

kept by a French ´emigr´e named Riebau, to whom the youth was apprenticed.

Faraday lived at this establishment for eight years, working as a bookbinder

and acquiring manual skills that later stood him in good stead in his experimental

work. In these years he was strongly influenced by a book by the

eighteenth-century divine Isaac Watts entitled On the Improvement of the

Mind. He followed its suggestions for self-improvement, such as the formation

of a discussion group with others of similar age who were interested

in the exchange of ideas. When his apprenticeship with Riebeau expired, he

went on to work for another French ´emigr´e, with whom he was less happy.

Faraday’s contemporaries describe him as proud, kind and gentle, simple

both in manner and in attitude and with extraordinary animation of

countenance. His voice was pleasant and his laugh hearty. In height, he was

somewhat below average. His head from forehead to back was so long that

his hats had to be specially made for him. In youth his hair was brown,

curling naturally; later in life it approached white and was always parted at

the centre. It was from his mother that he acquired much of his character,

114 From Ohm to Helmholtz

especially the rejection of all social and political distinctions. His parents

were both Sandemanians, as he became himself. After the Restoration John

Sandeman, with his father-in-law John Glas, had seceded from the Presbyterians

and founded this small religious sect, which stressed the love of the

Creator. Sandemanians believe in the literal truth of the Scripture, pledging

themselves to live according to the Bible and in imitation of Christ.

Faraday’s interest in science was first aroused by a chance reading of

the article ‘electricity’ in a copy of the Encyclopaedia Britannica that he

was rebinding. The article, which was written by one James Tytler, was

somewhat heretical in its views, but it stimulated Faraday to try to verify

the statements in it, and much later the influence of Tytler’s unorthodox

theories regarding the nature of electricity was still apparent. Meanwhile

he took advantage of some of the lectures on scientific subjects being given

in London, especially those given by a certain John Tatum, who gathered

together a group of young men at his home every Wednesday night to discuss

scientific matters and make use of his library. They called themselves

the City Philosophical Society; this group seems to have played a part in

the foundation of Birkbeck College. In this way Faraday obtained a basic

scientific education, covering electricity, galvanism, hydrostatics, optics,

geology, theoretical mechanics, chemistry, astronomy and meteorology.

It was chemistry that interested Faraday most at this stage in his

career. Here he set great store by Jane Marcet’s book Conversations on

Chemistry, Intended more Especially for the Female Sex. This popular work

had been much influenced by the lectures of Davy which she had attended at

the Royal Institution. A customer of Riebau’s gave Faraday tickets to attend

Davy’s lectures himself. He went and from the gallery took careful notes;

thereupon he adopted Davy as his role model. Soon an accident opened up

an opportunity for him to leave the craft of bookbinding behind him and

begin a scientific career. Davy had temporarily been blinded as a result of

an explosion during a chemical experiment, so he needed an amanuensis.

Faraday was recommended to Davy, who was much impressed by his work.

When Davy’s assistant at the Royal Institution was dismissed for misconduct

in 1813, Faraday was appointed in his place.

Davy was a close friend of Coleridge, who brought to England the

philosophical ideas of Kant and his followers. These ideas helped to provide a

unity to Davy’s work, and even more strongly that of Faraday, because it was

in tune with his religious beliefs. His science was characterized by brilliant

flashes of insight soundly supported by experimental evidence. Davy exerted

a most important influence on Faraday’s intellectual development, which

Michael Faraday (1791–1867) 115

took place gradually. In the autumn of 1813 Davy and his wife went abroad

on an extended honeymoon, taking Faraday with them as factotum. The

party went to France, Switzerland and Italy, calling on eminent men of

science, such asAmp`ere andVolta, wherever possible. Unfortunately Davy’s

wife, who was something of a snob, insisted on treating Faraday as a personal

servant. On their return to London, after eighteen months on the continent,

Faraday began to try his hand at experimental work; encouraged by Davy, he

published his conclusions in the Quarterly Journal of Physics, until in 1820

he had a paper accepted for the more prestigious Philosophical Transactions

of the Royal Society.

About this time Faraday made the acquaintance of Sarah Barnard, the

sister of one of the friends he had made at the City Philosophical Society,

and they were married in 1821; she was twenty-one, he twenty-nine. Like

him she came of a Sandemanian family; Sandemanians tended to marry, and

to find most of their social life, within the sect. Soon after marriage Faraday

became a full member of the sect, which played such an important part in

his life, and made his confession of faith, later becoming a Deacon and later

still an Elder, one of three responsible for the administration of the church

in London. ‘A just and faithful knight of God’, said his fellow-scientist John

Tyndall, ‘I think that a good deal of Faraday’s week-day strength and persistency

might be referred to his Sunday Exercises. He drinks from a fount

on Sunday which refreshes his soul for a week.’ Exclusion from the church

was a severe punishment, which he suffered on at least one occasion.

By this time Faraday hardly needed Davy’s patronage any more. Davy

was never able to accept Faraday as a social equal, whereas John Herschel,

son of the great astronomer, readily did so. When the two men first met

Faraday was still a lowly assistant at the Royal Institution, whereas

Herschel, his junior by six months, was a graduate of Cambridge, where he

had been senior Wrangler and Smith’s prizeman, and was already a fellow

of the Royal Society. They became firm friends and Herschel never failed

to provide Faraday with encouragement and support when necessary. For

example, he was one of the first to sign the certificate nominating Faraday for

the fellowship of the Royal Society, whereas Davy, who was president at the

time, made strenuous efforts to have the nomination withdrawn. Exactly

why Davy did so is unknown, but Faraday was nevertheless elected fellow

in 1823. Davy nominated Faraday for the position of secretary of the newly

founded club, the Athenaeum; however, as soon as the club had become well

established he resigned the office of secretary while remaining an ordinary

member.

116 From Ohm to Helmholtz

The next twenty years saw Faraday make one scientific discovery

after another, initially in chemistry and later in electricity, where his classic

investigations laid the foundations for the science we know today. His

earliest scientific work was on the liquification of gases, in 1823; his first

major contribution to science, the discovery of benzene, followed two years

later. However, it is with electricity and especially electrochemistry that

his name is permanently linked. After discovering the process of electrolysis

in 1832, he went on to work out the laws which control it, no mean

feat for a scientist without mathematical training. He was thirty when he

discovered electromagnetic rotations, forty when he discovered induction,

using it to produce the first electrical generator and transformer, and fiftyfour

when he discovered the magneto-optical effect and diamagnetism. Not

many scientists have begun their creative lives so late or continued so long.

Faraday’s most famous work is his Experimental Researches in Electricity,

in three volumes, made up of papers that had mostly originally appeared

in the Philosophical Transactions or the Philosophical Magazine. This was

followed by his similar Experimental Researches in Chemistry and Physics.

By 1825 the financial position of the Royal Institution left much to be

desired. Faraday helped to strengthen it by instituting the celebrated series

of Friday evening discourses, of which he gave over a hundred himself. These

served to educate the English upper class in science, particularly those of its

members with influence in government and the educational establishment.

To prepare himself for lecturing, at which he excelled, Faraday took lessons

in elocution, and he had some experience as a preacher, but these were

of little importance compared with the care he took over preparation and

presentation. He thought that, even though a lecture might be written out,

it should not be read to the audience. His influence as a lecturer consisted

less in the logical and lucid arrangement of his materials than in the grace,

earnestness and refinement of his whole demeanour. ‘Except by those well

acquainted with his subjects, his Friday evening discourses were sometimes

difficult to follow’, said Tyndall, ‘but he exercised a magic on his hearers

which often sent them away persuaded that they knew all about a subject of

which they knew but little.’ One of his auditors spoke of his gleaming eyes,

the hair streaming out from his head, his moving hands and his irresistible

eloquence: his audience took fire with him and every face was flushed.

Another commented that ‘no attentive listener ever came away from one of

Faraday’s lectures without having the limits of his spiritual vision enlarged,

or without feeling that his imagination had been stimulated to something

beyond the mere exposition of physical facts’.

Michael Faraday (1791–1867) 117

The Faradays lived in rooms over the Royal Institution, known as the

Upper Chambers, from which a back staircase led directly to the laboratory

in the basement, where he enjoyed good facilities for his experimental

work. He gave regular courses, in addition to the routine lectures, and was

heavily involved in the organization of the various activities of the Institution,

of which he was effectively administrator. From 1829 to 1852 he also

held the position of professor of chemistry at the Royal Military Academy

at Woolwich. He was also greatly in demand to give practical advice, commercial

analysis, expert testimony and public service generally. In 1836, for

example, he became chief scientific adviser to Trinity House, the ancient

foundation responsible for the erection and maintenance of coastal installations

such as lighthouses and buoys; the electrification of lighthouses was

just in its early stages. He gave advice on the prosecution of the war against

Russia. In 1841, faced with too many calls on his time and energy, Faraday

experienced a nervous breakdown; he had previously sometimes suffered

from loss of memory and dizziness. Memoranda written by Faraday at

this time show that his mind was seriously disturbed; there is a theory

that his condition might have been due to mercury poisoning. He went to

Switzerland accompanied by his wife, who was also in poor health, and his

brother-in-law the watercolourist George Barnard. As soon as his health permitted

he resumed scientific work, this time on magnetism, but the important

discoveries all precede the breakdown. There is a parallel with Isaac

Newton, who also experienced a nervous breakdown, but, unlike Faraday,

Newton never recovered his scientific drive.

In early days Faraday had added to his unduly modest salary from the

Royal Institution a supplementary income from what he called ‘commercial

work’. This supplement might have become important to him, but just

as it showed signs of expansion Faraday abandoned it. The fall in his commercial

income was correlated with his discovery of magneto-electricity,

when worldly gains became contemptible compared with the rich scientific

landscape which opened up before him. In 1835 the Tory Prime Minister

Sir Robert Peel wished to offer Faraday a Civil List pension, but, following

a change of government, it fell to the Whig Lord Melbourne to make the

offer, which he did with such ill-grace that the proud Faraday felt insulted

and turned it down. When this became public knowledge there was uproar;

the King intervened, Melbourne apologised and Faraday accepted the pension

of £300. Among the honours he received from other countries was

membership of the Legion of Honour and a knighthood from the King of

Prussia; also he was a foreign member of the Paris Academy.

118 From Ohm to Helmholtz

Faraday maintained a strict separation between his religion and his

science, but both were of the utmost importance to him. The tenderness of

his nature made it difficult for him to resist the appeal of distress, but he

preferred to distribute his charitable gifts through some organization that

assured him they would be well bestowed. Faraday had been interested in

the visual arts from an early age and was personally acquainted with some of

the leading artists of his day. He gave advice on the conservation of works

of art to institutions such as the British Museum, the National Gallery

andWestminster Abbey. He collected drawings, engravings, lithographs and

photographs of scientists and other notables of his day. Although himself

not one of the pioneers of photography, he was much interested in this new

development.

By the middle of the 1850s Faraday had gone as far in research as he

could, and, as we shall see, his work was taken up by the young Scotsman

Clerk Maxwell, whose theory of the electromagnetic field built on the foundations

that Faraday had laid. In fact he, before others, noticed the failing

strength of his brain and declined to impose on it a weight greater than it

could bear. His mind deteriorated rapidly, and, even if he had been able

to understand Maxwell’s mathematics, it is doubtful whether he would

have been able to follow Maxwell’s reasoning and appreciate these new

developments.

As his mental faculties declined, Faraday retreated gracefully from

the scientific world. He turned down invitations to accept the presidency

of the Royal Society and that of the Royal Institution; he found the idea of

the latter position so upsetting that it brought on another nervous crisis.

He concentrated what remained of his energies on his teaching functions at

the Royal Institution. It was more in his Christmas lectures to audiences

of children, rather than in those he addressed to adults, that his unequalled

ability as a teacher was most in evidence. His Christmas lectures for a juvenile

audience for 1859/60, on the various forces of matter, and for 1860/61,

on the chemical history of a candle, were edited by William Crookes and

have become classics. However, even his lecturing abilities began to fade,

and he was forced to abandon the lectern in 1861, after experiencing fits of

giddiness and loss of memory. He arranged for Tyndall to deputise for him

at the Royal Institution. In the closing years of his life the Faradays lived at

Hampton Court, not in the palace but in a house on the Green placed

at his disposal by Queen Victoria at the suggestion of Albert, the Prince

Consort. Michael Faraday died in his seventy-fifth year on August 25, 1857

from ‘decay of nature’; at his own request he was buried without pomp or

George Green (1793–1841) 119

ceremony in a simple grave in Highgate cemetery. ‘A mighty investigator,’

said Tyndall at his funeral, ‘nothing could equal his power and sweetness as

a lecturer.’ His wife Sarah died in 1879; they left no descendants.

George Green (1793–1841)

In 1828 an essay entitled The Application of Mathematical Analysis to the

Theories of Electricity and Magnetism was published. The author was a

largely self-educated thirty-five-year-old miller named George Green. The

Essay attracted little attention at the time but is now regarded as one of the

landmarks of modern mathematical physics. The story of his life is one of

the most remarkable in this collection.

A baker named George Green lived in Nottingham, a historic town

in the Midlands of England. In 1791 he married a woman named Sarah

Butler. Her father helped him set up a bakery in the town centre. Their

only son, also named George, was born on July 14, 1793. Two years later

their daughter Ann was born; she later married a cousin, William Tomlin,

who is the source of most of what is known about the life of the future

mathematical physicist.

George Green junior was eight years old in 1801 when he went to

Robert Goodacre’s Academy, the best school in the town. Goodacre wrote

textbooks on arithmetic and in later years would travel in Britain and the

USA giving lectures on popular science. On the roof of the building he constructed

an astronomical observatory. The school was well equipped with

scientific instruments, and probably the boy learned to use them in the

short time he was at the school. We know that, when it was enlarged some

years later, it offered teaching in reading, English grammar, penmanship and

arithmetic. Young Green was probably taught these. It also offered geography,

the use of globes, mathematics, book-keeping, English composition,

natural philosophy, astronomy, history, Latin and Greek. French was taught

by a native; there seems no doubt that the boy learned some French at some

stage. Later Tomlin wrote that his ‘profound knowledge of mathematics’

soon exceeded his schoolmaster’s.

Not many of the pupils at the Academy stayed more than a year or

two, so it was unremarkable that the boy was withdrawn after four terms.

Then, at the age of nine, he started work in his father’s bakery. The business

was prospering and George Green senior, who already owned some houses

in Nottingham itself, was able in 1807 to purchase an attractive plot of land

in the nearby village of Sneinton, only a mile from the town centre. The land

stood on a hill, and on this site he built a ‘brick wind corn-mill’. The mill

120 From Ohm to Helmholtz

itself, which stood fifty feet high, was surrounded by auxiliary buildings,

including a house for the miller. This was occupied by a manager, while the

family continued to live in Nottingham and run the bakery.

Some ten years later George Green senior built a substantial family

house alongside the mill, with two front rooms and five bedrooms, and

moved there with his wife and son. As Tomlin tells us, the son ‘lived with

his parents until the termination of their lives and duly rendered assistance

to his father in the prosecution of his businesses’. When George Green senior

died in 1829 at the age of seventy, his wife having predeceased him by four

years, he left money and his Nottingham property to his daughter Ann

Tomlin and the milling business to his son. There was nothing romantic

about being a miller. It was exhausting work; moreover, the dust from the

operation accumulated in the lungs and caused a disease similar to silicosis.

Tomlin goes on to say that the work was ‘irksome to the son who at a very

early age and with in youth a frail constitution pursued with undeviating

constancy, the same as in his more mature years, an intense application

to mathematics or whatever other acquirements might become necessary

thereto’.

We must now go back some years to 1823, when George Green senior

was still alive. This was a period when the industrial and scientific revolution

had led to the formation of various intellectual and cultural institutions

in some of the more enterprising English towns. In Nottingham such

an institution was located in a building called Bromley House, and known

by that name. It had been founded in 1816 and soon became the popular

venue for the wealthier citizens, the leisured, the cultivated and the philanthropic.

It was a meeting-place for the committees of the newly formed

Nottingham School of Medicine and of the Ladies’ Bible Society, the Literary

and Debating Society, the Geological, the Natural History, the Geographical

and the Astronomical Societies. The Amateur Musical Society also

met there; artists exhibited there. However, most importantly, there was

a library, called the Nottingham Subscription Library, which non-members

could use for a fee. When Green became a member there were about a hundred

subscribers, who were mainly members of the leading town and county

families or the more prominent local firms. There were also professional

men, doctors, lawyers and so on.

Originally £600 had been spent on books for the library, but further

purchases were made, and members could ask for particular books to be

ordered. They were mostly in the categories of literature, history and biography,

with some travel and natural history. When Green was a member, the

George Green (1793–1841) 121

catalogue listed no more than a dozen serious scientific and mathematical

works, including treatises by Lagrange and Laplace, but none of them are

the particular books to which Green refers or makes use of in the Essay.

There was, however, a set of the Philosophical Transactions of the Royal

Society. In its pages Green would have been able to follow the course of

discoveries in science for the previous 160 years.

At the same time, one has to ask what was happening between the

time he left school, at the age of nine, and the time he joined the library, at

the age of thirty?We know that he worked in the bakery and the mill, but it

seems he used to retreat to a room on the top floor of the mill to study whenever

he could. If someone was guiding his studies, the most likely candidate

seems to be Toplis, headmaster of the Free Grammar School in Nottingham.

Toplis was the second head who was a Cambridge graduate in mathematics.

He was in his twenties when he came to Nottingham and stayed until 1819,

by which time Green was twenty-six. After that he returned to Cambridge

as a fellow of Queens College. (The college library contained a good collection

of books on mathematics in which the French mathematicians of

the time were particularly well represented.) The methods Green used are

distinctively French. As well as with Laplace’s magnum opus, he seems to

have become familiar with papers by Biot, Coulomb and Poisson, among

others.

Toplis was among the few who recognized that Britain was being left

far behind in the field of mathematical research after more than a century of

steady progress on the continent, particularly in France. He was an enthusiast

for the work of the French school and had translated the first two

books of Laplace’sM´ecanique c´ eleste into English. His translation was published

in Nottingham in 1814, when Green was twenty-one, and Toplis

presented a copy to the Nottingham Subscription Library when he became

a member. Until about 1817 the Green family lived very close to the Free

Grammar School, where Toplis was resident. Although there is no certainty

that Toplis was Green’s mentor, the circumstantial evidence is persuasive.

Five years after Green joined the library his first and greatest work, the

Essay on Electricity and Magnetism, was published in Nottingham by private

subscription in 1828. There were 51 subscribers, half of whom were

fellow members of Bromley House. It was one of the first attempts to apply

mathematical analysis to electrical phenomena and was of such importance

that it has been described as the beginning of modern mathematical physics

in Britain. In it Green gave the name potential to Laplace’s analytical device

and used it in relation to electricity, where it proved an invaluable tool in the

122 From Ohm to Helmholtz

development of electromagnetic theory. The Essay is also important for the

introduction of new mathematical techniques, known nowadays as Green

functions, which are regularly used throughout mathematical physics, and

Green’s theorem, which is fundamental in differential geometry as well.

Such a seminal work should have been published by one of the learned societies,

rather than in such an obscure way, but Green seems to have thought

it would not be accepted, ‘coming from an unknown individual’. Unfortunately

the result was that the Essay attracted little attention, and, greatly

discouraged, Green seems to have given up his investigations for the next

few years.

Green now had full responsibility for running the family business,

which he had inherited. Like his father, however, he relied on a manager,

named Smith, who had a daughter, Jane, who was nine years younger than

Green. When she was twenty-two she bore him a daughter, Jane, who was

known as Jane Smith, like her mother. Later two sons and three daughters

were born and known by the surname of Green, although the parents never

married; only the first daughter was known by the other surname.

One day in January 1830 Green had a conversation with a certain

Mr Kidd from the city of Lincoln, which had highly significant consequences.

Green had dedicated his Essay to the Duke of Newcastle, who

controlled the representation of Nottingham in Parliament. He had also

sent a copy on publication to a subscriber living near Lincoln, Sir Edward

Ffrench Bromhead, who replied most encouragingly and apparently offered

to send any further mathematical work by Green to one of the learned societies.

Unfortunately the diffident Green did not take up this offer – someone

apparently told him it was just a polite gesture – but Kidd assured him that

it was intended seriously. So, nearly two years after publication of the Essay,

Green wrote a long, apologetic letter to Sir Edward explaining the reason

for the delay and promising to take up the offer if it still held good. This

started a correspondence between the Lincolnshire baronet, himself a mathematician,

and Green, who seems to have visited his seat of Thurlby Hall

on several occasions.

Sir Edward had been one of the Cambridge students who founded the

Analytical Society in 1819. This body, which later became the Cambridge

Philosophical Society, helped to rescue Cambridge science from its torpid

condition. After graduating from Cambridge in 1812, he studied law at the

Inner Temple and, on returning to Lincolnshire, began playing a prominent

part in city and county affairs. However, he retained his Cambridge

connections and invited Green to accompany him on a visit to his alma

George Green (1793–1841) 123

mater. Green declined: ‘You were kind enough to mention a journey to

Cambridge on June 24th to see your friends Herschel, Babbage and others

who constitute the chivalry of British science. Being as yet only a beginner

I think I have no right to go there and must defer that pleasure until I

shall have become tolerably respectable as a man of science should that day

ever arrive.’ The possibility of going up to Cambridge as an undergraduate

had already been mentioned by Green in April of that year. He naturally

turned to Sir Edward for advice as to ‘which college would be most suitable

for a person of my age and imperfect classical attainments’. Unsurprisingly,

Sir Edward recommended his own college, Gonville and Caius. In preparation

for his move to Cambridge, Green, having leased the mill after his

father’s death, let the family house: we have no information on the whereabouts

of Jane, who by this time had four children. He resigned from the

Nottingham Subscription Library, having had the satisfaction of presenting

a copy of his first memoir published in Cambridge the previous year.

By the end of 1833 Green had written three memoirs. Two were published

by the Cambridge Philosophical Society and one by the Royal Society of

Edinburgh.

Green arrived in Cambridge early in October 1833 and was admitted

as an undergraduate to the college usually known as Caius (pronounced

keys), a community of some 170 students and twenty fellows. He was much

older than the normal age of admission. On his departure for Cambridge,

Sir Edward had given him letters of introduction ‘to some of the most distinguished

characters of the university that he might keep his object steadily

in view under some awe of their names and look upwards, not of course

with any view of trespassing on the social distinctions of the university,

in my time more marked than at present, but that he might venture to

ask for advice under any emergency’. Green managed to pass the general

examination in Latin, Greek and ecclesiastical history. After the first eight

months he wrote to Sir Edward: ‘I am very happy here and am I fear too

much pleased with Cambridge. This takes me in some measures from those

pursuits which ought to be my proper business, but I hope on my return to

lay aside my freshness and become a regular Second Year Man.’

The Senate House (or Tripos) examination dominated the undergraduate

course. It consisted of 200 questions to be answered over seven days

in midwinter in the unheated building. The first three days were on book

work, the books being the Elements of Euclid and the Principia, and passing

on these was sufficient for most students. For the better students it was

just a question of speed. However, for those aspiring to honours there were

124 From Ohm to Helmholtz

four more days of more difficult problems over a wide range of subjects. The

lectures were optional; for most students the bulk of the instruction came

from a private tutor or coach, but it is unlikely that Green could afford this

extra expense.

Green achieved fourth place on the order of merit in the notorious

examination and thereby became eligible for a college fellowship. As soon

as a vacancy occurred, two years later, he was elected. Fellowships carried

the right to rooms in college and meals at the common table, free of charge,

and a small stipend. His duties were far from onerous. He is known to

have set and supervised examinations; his manner on such occasions was

recorded as gentle and pleasant. As a Cambridge graduate he could attend

meetings of the Philosophical Society and present his papers there in person.

Three papers of his were published in 1838 and three more the next year.

Two were on hydrodynamics, two were on the propagation of light and two

on the propagation of sound. Thus Green had altogether eight papers published

in Cambridge, one in Edinburgh and, of course, the original Essay in

Nottingham. The Essay, on electricity and magnetism, and the last memoir

on the propagation of sound are considered to be his most important works.

During his six years at the university he had achieved a considerable reputation.

‘He stood head and shoulders above all his contemporaries inside

and outside the university’, wrote someone who was there at the time.

Yet only six months after his admission to the fellowship at the end

of October 1839 he took the coach home to Nottingham for the last time.

In the words of his cousin Tomlin: ‘He returned, indisposed after enjoying

many years of excellent health in Sneinton, Alas! With the opinion that he

should never recover from his illness and which became verified in little

more than a year’s time by his decease on May 31, 1841.’ For all his six

years in Cambridge and his reputation there, Green came home to die in

relative obscurity. All the local newspaper had to say was the following: ‘we

believe he was the son of a miller, residing near to Nottingham, but having

a taste for study, he applied his gifted mind to the study of mathematics, in

which he made rapid progress. In Sir Edward Ffrench Bromhead, Bart., he

found a warm friend, and to his influence he owed much, while studying

at Cambridge. Had his life been prolonged, he might have stood eminently

high as a mathematician.’

Green died of influenza aged forty-seven, in a house in Nottingham

occupied by his partner Jane Smith and her family of seven children. Clara,

the youngest, had been born the previous year, only a few weeks after his

final return from Cambridge. Jane Smith was the one who reported his

Joseph Henry (1797–1878) 125

death; and she was with him at the end. He was buried with his parents

in St Stephen’s churchyard in Sneinton. On the gravestone he is described

as ‘Fellow of Caius College, Cambridge’. In the will he had made some

ten months previously, he describes himself as ‘late of Sneinton in the

County of Nottingham and now of Caius College, Cambridge, Fellow of such

College’. Whatever the immediate cause of death, it seems most likely that

the ‘indisposition’ which caused him to return home was the miller’s version

of silicosis, although Felix Klein, in his account of the development of

mathematics in the nineteenth century, attributed it to alcoholism; perhaps

he heard this from Green’s contemporary the mathematician James Joseph

Sylvester.

In time the mill at Sneinton fell into disrepair. Any papers that Green

may have left seem to have been destroyed. His descendants were unaware

of their genius of an ancestor. Recently, however, the city has begun to take

pride in one of its most distinguished citizens. The mill has been restored

and a little museum added, in which one may learn about Green’s work and

its consequences, and perhaps purchase some flour ground at the mill. When

the bicentenary of Green’s birth occurred in 1993, scientific conferences

were held to discuss the influence of his work, and a ceremony was held at

Westminster Abbey, where a simple plaque was unveiled in his memory. It

can be found near the base of the monument to Newton.

Joseph Henry (1797–1878)

The American physicist Joseph Henry made important contributions to the

investigation of electromagnetism. He built the largest electromagnet then

known, which could lift 300 kilograms; he also discovered electromagnetic

induction, independently of Faraday, and invented an early formof the telegraph

and the electrical relay. On principle he never patented any of his

inventions, which when exploited commercially made others rich but not

the inventor. The unit of inductance is named after him. Sadly, his recognition

as a great experimental physicist arrived too late to afford him any

satisfaction. Instead it was rather his wise administration of the newly established

Smithsonian Institution that made him famous.

Joseph Henry was born in Albany, the state capital of New York,

on December 17, 1797. His father William Henry was a sometime day

labourer from Argyle, distantly related to the earls of Stirling, while his

mother Ann (n ´ee Alexander) was the daughter of a miller. William Henry

died young, and it was chiefly his widow Ann who brought up her son.

She was a small woman with delicate, rather beautiful features, who lived

126 From Ohm to Helmholtz

to an advanced age. She was a devout and strict member of the Scottish

Presbyterian Church, the principles of which she passed on to her son. Before

he had turned six she sent him to nearby Galway to live with her stepmother

and her twin brother John. After three years of elementary school Joseph got

a job in a general store, where the storekeeper, an educated man, encouraged

him to continue with his education after work. When the boy was

approaching fourteen he returned home to Albany, where he was apprenticed

to a watchmaker and silversmith. After the business had failed he

was released from his apprenticeship, but not before he had acquired some

practical skills that were to be useful to him later.

Although Albany was not a large place in those days, it boasted an

unusually good theatre, which for a year occupied most of the young man’s

leisure hours. He belonged to an amateur group for which he acted, produced

and wrote plays. This experience may have helped in later years when he

needed to be an effective public speaker. During this period Joseph Henry

is described as being remarkable for his good looks, delicate complexion,

slight figure and vivacious nature. His lively temperament made him a general

favourite. The town had an excellent school, almost a college, called the

Albany Academy, where Joseph Henry continued his education by attending

night classes in geometry and mechanics, followed by calculus and chemistry,

while supporting himself by working as a private tutor and doing a

Joseph Henry (1797–1878) 127

little teaching. He was inclined towards science, but in the USA the only

career open to a scientist at this time was in medicine.

Albany also possessed a scientific society, the Albany Institute, with

a miscellaneous library of some 300 volumes. Henry obtained the post of

librarian and gave a few lectures to the members, complete with experimental

demonstrations. Meanwhile he was studying the classicM´ecanique

analytique of Lagrange. The versatile young man also led a grading party for

a new highway running from the Hudson River to Lake Erie. His success in

this work brought him offers of similar positions elsewhere, but he turned

them down in favour of the post of professor of mathematics and natural

philosophy at Albany Academy in 1826. This meant that he had to renounce

his earlier idea of becoming a physician, but he had not got very far with

that.

Henry was now on the threshold of the scientific career which was

to bring him such distinction. He would have read Priestley’s History and

Present State of Electricity and might also have been aware of Coulomb’s

work. Perhaps he also knew of Amp` ere’s work and of Volta’s invention of

the battery, as a source of electric current. In any case, Joseph Henry spent

a good deal of his spare time in the useful exercise of repeating the classic

experiments.

A maternal uncle of Henry’s, a successful businessman in Schenectady,

had died and his widow had brought her family to live in Albany. Her

son Stephen was a delicate and sensitive youth, who at the age of eighteen

had graduated from Union College with high honours in mathematics and

astronomy. Since they had similar interests the two cousins saw much of

each other; soon Stephen was also on the faculty of the Academy and later

he would follow Henry to Princeton. Meanwhile Henry had been courting

Stephen’s sister Harriet, and they were married by the end of 1829. They had

six children, of whom two died in infancy and the only son on the threshold

of manhood. The three survivors, Helen, Mary and Caroline, were to

brighten their parents’ declining years. Modest, retiring and understanding,

Harriet furnished a home life into which Henry could retreat from the pressures

of the outside world. She seems to have been an ideal wife for him.

In his thirty-sixth year Henry was appointed to the chair of natural

philosophy at the College of New Jersey, which would become Princeton

University many years later. He started work there in 1832. The college

was at a low ebb, with only about seventy students, but the situation was

beginning to improve and later Henry was to say that the fourteen years

he spent at Princeton were the happiest of his life. When he first arrived

128 From Ohm to Helmholtz

there was general amazement at his appearance: ‘His clear and delicate complexion,

flushed with perfect health, bloomed with hues that maidenhood

might envy. Upon his splendid front, neither time nor corroding care, nor

blear-eyed envy, had written a wrinkle nor left a cloud; it was fair and pure

as monumental alabaster. His erect and noble form, firmly and gracefully

poised, would have afforded to an artist an ideal model of Apollo.’

One advantage of the move to Princeton was that it brought him into

contact with a wider circle of men engaged in scientific research. No longer

was he obliged to work in an intellectual vacuum. For example, a short

journey on the newly opened railroad brought him to Philadelphia, seat

of another university and home of several learned societies. One of them

was the American Philosophical Society, to which he was elected in 1835.

It was to the members of this society that he communicated the results

of his Princeton researches. Unfortunately the society was rather slow in

publishing papers presented to it, so Henry was continually at a disadvantage

in the competition with Faraday, who took no interest in what was being

done in America.

It is interesting to compare the lives of Henry and Faraday. The

former was born in 1791 and died in 1863, the latter was born in 1797

and died in 1878; but their periods of peak productivity were almost identical.

They both sprang from the same working class that had no traditions

of study and that did not possess the means of educating its children. Both

were influenced to follow a scientific career by the chance reading of books

that revealed the works of nature to the imagination. They were both deeply

religious men who regarded nature as the handiwork of their Creator. However,

no comparison of the two would be complete without reference to

their relative situations at this stage of their careers. We have seen Henry

at work in a small town, with only very little spare time, hampered for

want of funds and facilities, with very few technical companions. Faraday

was much more favourably situated at the Royal Institution, living in the

world centre of intellectual activity, with as much time as he wanted for

research, in constant communication with some of the most brilliant technical

minds of the day. Henry found that his discoveries were anticipated by

Faraday over and over again; he became understandably disappointed and

discouraged.

In 1836, in recognition of his work during his first four years at Princeton,

the trustees of the college granted Henry a year’s leave of absence on

full salary. It was a good time to escape from the USA, for the nation was just

entering upon a financial depression. England by then was in many respects

Joseph Henry (1797–1878) 129

a different country from the one against which the American colonists had

rebelled. Reform was in the air, and the spirit of industry had taken a firm

grip on the people. Although London was his destination, Henry began his

journey by first going toWashington, to collect some letters of introduction;

he was not impressed by the federal capital, where he was destined to spend

so much of his life.

Once in London Henry lost no time in visiting the Royal Society and

the Royal Institution. Unfortunately it was the Easter vacation and Faraday

had just left town, but they met before long, and Henry heard Faraday

lecture. After two useful and enjoyable months, he moved on to Paris for two

more weeks. Observing the passing scene, he found many Gallic customs

curious and was struck by the way women were engaged in many occupations

followed only by men in America. He deplored the prevailing military

spirit, particularly the obligation for every able-bodied male to serve one day

each month on military duty. After brushing up his French, he met a few of

the French men of science and attended a meeting of the Paris Academy, but

otherwise he seems to have made little real contact with the leading French

scientists. Finally, after a short visit to the Netherlands, he returned to

London to stay with his former student Henry James, father of the psychologist

William and of the well-known novelist.

Both Joseph and Harriet being of Scottish descent, like so many New

Englanders, they took the packet to Edinburgh and called on many of the

notables there as well as elsewhere in Scotland. He ended his tour in

Liverpool, where the meeting of the British Association was in progress. On

his return to America, Henry felt well informed about the state of physics

in Europe, especially experimental physics and the teaching of science. He

came back in excellent form, strong and fervent, charged with enthusiasm to

resume his own investigations into electromagnetism. For ingenuity, completeness

and novelty in the examination of new phenomena, these next

researches serve as a model for the experimental physicist. Their significance

lies not so much in the material which he added to science as in the

new territories he opened to the view of those who followed in his footsteps.

Henry had now reached his forty-ninth year. All the high promises

that had accompanied him to Princeton had been fulfilled in the fourteen

years he spent there. He had found congenial companions and duties

well suited to his powers. He had been valued and honoured by members

of the faculty, while the students held him in reverence. Although far

from exhausted scientifically, rather at the height of his powers, he chose

to withdraw from active scientific work and become an organizer and

130 From Ohm to Helmholtz

administrator. The occasion which brought about the change was his decision

to accept the post of secretary to the Smithsonian Institution. With

complete philosophical detachment he had evaluated the needs of American

science and threw in his lot with the new venture to promote the satisfaction

of those needs.

To understand how it came about that a man who was not American

and had no connection with the USA should have founded this great

American institution, it is necessary to say something about the life of the

founder. James Smithson, known in his youth as James Lewis or Luis Mace,

was the illegitimate son of Hugh Smithson, first Duke of Northumberland

of the third creation, and the wealthy and high-born Elizabeth Mace. He

was born in France in 1765, matriculated at Oxford University as a member

of Pembroke College at the age of seventeen and early displayed a taste for

science that never left him. After having been admitted as a fellow of the

Royal Society in 1787, he read papers to that body and published a number

of them, chiefly on chemistry and mineralogy. He already knew most of the

notable men of science of his time, such as Arago in Paris and Cavendish in

London. He spent most of his later life on the continent of Europe, associating

with the men of science in Berlin, Paris, Rome, Florence and Geneva,

but eventually settled in the French capital, although he was in Genoa when

he died. Apparently the reason he left England was that, because of the illegitimacy

and the refusal of his father to acknowledge their relationship, he

never received the social recognition to which he believed he was entitled.

Also perhaps he had too high an opinion of his own abilities and a tendency

to flaunt his wealth.

In his will, made when he turned sixty, Smithson left a life interest

in his considerable fortune to a nephew, after which it should pass to the

‘United States of America, to found at Washington, under the name of the

Smithsonian Institution, an Establishment for the increase and diffusion of

knowledge among men’. Previously he had intended to leave his fortune to

the Royal Society, and it is something of a mystery just why he changed

his mind. After some discussion the bequest was accepted by Congress and

before long over 100 000 gold sovereigns were delivered to New York. Thereupon

there was great debate, extending over nine years, on how precisely

this princely legacy should be used. Eventually it was agreed that there

should be a library, a museum and an art gallery.

At the end of 1845 Henry was appointed secretary and first director

of the new institution. He took up office within days. Most of his

friends advised him against moving to Washington, pointing out his lack of

Joseph Henry (1797–1878) 131

experience in administration and organization, and Henry himself felt no

great enthusiasm about accepting the appointment, recalling the case of

Newton, who made no discoveries after becoming Warden of the Royal

Mint. The Princeton authorities promised him that they would welcome

his return if he decided he had made a mistake. His intentions were of the

best, but it soon became all too clear that members of Congress were going

to interfere and create problems. His immediate problem was to prevent the

capital of the endowment being plundered, for example on a grandiose building,

through the over-ambitious plans of Congressmen. Almost at once he

was offered a chance to escape when he was offered a chair at the University

of Pennsylvania; although this was probably the most desirable scientific

position the country had to offer, ideal for his needs, he turned it down,

greatly to the loss of science, as he did subsequent offers. Henry hoped that

he would be able to return to experimental work once the Smithsonian got

under way, but that was never a real possibility.

Before long the many-turretted red sandstone building in vaguely

Romanesque style known as the Castle was under construction, on a site

in the Washington Mall close to malodorous water and far from the residential

area of the city. Henry began to organize a series of publications

and a system of exchanges with other institutions that enabled the library

to develop. The subjects in which he took an interest are bewildering in

their variety. For some, such as meteorology, he was enough of an authority

himself, but for others, such as zoology, he consulted outside experts.

Increasingly the federal government used the Smithsonian as an all-purpose

institution, for example in designing the land surveys and expeditions which

were so necessary for the exploration of the American continent. Advice was

freely given when telegraph lines were being laid or railroads being planned.

Neither was the work confined to the USA. Today the Smithsonian Institution

comprises the largest complex of museums and art galleries in the

world.

The family, consisting of Joseph, his wife and the three daughters,

lived in the Castle itself, where they entertained liberally. The building

was badly damaged by fire in 1865 and much valuable material destroyed,

including Smithson’s voluminous papers and mineralogical collection, as

well as Henry’s correspondence and research notes. After the end of the

American Civil War he made another visit to Europe with his daughter

Mary. He continued in his various offices until the age of eighty and was

still at work at the end of 1877 when he found one morning that his right

hand was paralysed. Nephritis, in those days incurable, was diagnosed, and

132 From Ohm to Helmholtz

he knew that he did not have long to live. Joseph Henry died in his sleep in

Washington on May 13, 1878 and was buried in the Rock Creek cemetery

in Georgetown. A bronze statue by William Wetmore Story, which stands

at the entrance to the Castle, was unveiled in 1883.

Henry played an active part in establishing the American Association

for the Advancement of Science, which dates from 1848. Fifteen years later

he became one of the original members of the National Academy of Sciences,

an exclusive body like the European academies, which was founded by

President Lincoln to provide technological advice during the Civil War.

Although Henry was regarded as the foremost physicist in his own country,

he found it difficult to understand why his work met with so little approbation

abroad. He missed the fame his discoveries warranted through not

publishing the results of his experiments in time; and when he reformed

his dilatory habit and became punctual in announcing his results, he

still remained inconspicuous because the vehicle he chose was relatively

unknown in Europe. By the time the international scientific world had

awakened to a recognition of his merit, he was already dead.

Hermann von Helmholtz (1821–1894)

Helmholtz was among the most versatile of nineteenth-century scientists.

He was both a physiologist and a physicist. He is famous for his epochmaking

researches on the physiology of the eye and ear, and he is also

famous for his definitive statement of the first law of thermodynamics.

Hermann Ludwig Ferdinand Helmholtz, to give him his full name, was

Hermann von Helmholtz (1821–1894) 133

born in Potsdam on August 31, 1821. His father, August Ferdinand Julius

Helmholtz, had served with distinction in Prussia’s war of liberation against

Napoleon and, after studying at the new University of Berlin, became a

senior schoolmaster at the Potsdam gymnasium, teaching German, classics,

philosophy, mathematics and physics. His mother Caroline (n´ee Penne), the

daughter of a Hanoverian artillery officer, was descended in the male line

from William Penn, the founder of Pennsylvania, and on her mother’s side

from a family of French refugees. She was described as being profoundly

emotional and of sharp intellect while excessively simple in appearance.

The future scientist was their eldest son; they had two younger daughters

and another son, Otto, born in 1833, as well as two other sons who died in

infancy.

Helmholtz was a delicate child who early displayed a passion for

understanding how things worked, but otherwise developed slowly. At the

age of seven he began his school education, moving up to the gymnasium in

the spring of 1832. There he made good progress generally but particularly

in the exact sciences, for which there was an excellent teacher. Although he

was keen on physics, he was persuaded by his father, who could not afford

university fees, to take up the study of medicine, entering the Friedrich

Wilhelm Medical Institute of Berlin in 1838. Students at the institute were

entitled to attend lectures at the university; he took full advantage of this

and also studied a great deal on his own. They also received some financial

support in return for a commitment to serve for five years as military surgeons

after they qualified. By 1842 Helmholtz had progressed sufficiently

to be appointed house-surgeon at a hospital and completed his doctoral thesis

on the structure of the nervous system in invertebrates, the histological

basis of nervous physiology and pathology.

The next step in his career was to discharge his obligation to serve as

a medical officer in the army. In 1843 he was appointed assistant surgeon to

the Royal Hussars at Potsdam. His duties with the squadron left him plenty

of spare time, which he devoted to science, for example by studying the

mathematician Jacobi’s great treatise Fundamenta nova functionem ellipticarum

and by continuing research in physiology. By 1847 he was fully

qualified in medicine and became engaged to a young lady of the distinguished

von Velten family named Olga; however, marriage could not take

place until he had secured a permanent appointment.

In July 1847 he revealed himself as a master of mathematical physics

when he unveiled his theory of the conservation of energy at a meeting of

the Physical Society. He was perfectly willing to concede that others had

134 From Ohm to Helmholtz

had somewhat the same idea, but he was the first to formulate the principle

clearly and demonstrate it conclusively by scientific methods. While it was

enthusiastically welcomed by the younger physicists and physiologists of

Berlin, the older scientists almost without exception rejected it. Among the

mathematicians Jacobi was one of those who unhesitatingly proclaimed the

significance of Helmholtz’ work.

In 1848, through the influence of Baron von Humboldt, Helmholtz

was released from the remainder of his military service to become lecturer at

the Academy of Arts and assistant in the Anatomical Museum in Berlin. He

held these positions only briefly, since the following year he was appointed

associate professor of physiology and director of the physiological institute

at the Albertina University of Ko¨ nigsberg, enabling him to marry. The next

year he published the first part of his classic work on measurements of

the time relations in the contraction of animal muscles and the rate of

propagation in the nerve; the second part followed two years later.

Early in 1851 Helmholtz invented the ophthalmoscope, a turningpoint

in the way his work was regarded. This little invention, which took

him only two months to design and construct, made him famous. Being

back in favour with the authorities, from then on he was left free to follow

the promptings of his scientific curiosity. He went off on a tour through the

Swiss Alps to northern Italy, where he was enchanted by Venice, returning

via Trieste and Vienna. En route he took the opportunity to call on the

leading scientists at the places he passed through. On his return he was promoted

to full professor at Ko¨ nigsberg; his inaugural lecture ‘On the Nature

of Human Sense Perceptions’ was a splendid example of his gift for making

difficult scientific problems, close to the frontiers of research, intelligible

to a general audience. This led to his famous physiological theory of colour

vision, based on ideas of Young.

Helmholtz and his wife were happy and settled in Ko¨ nigsberg. They

were cheerful and contented, serious and industrious yet averse to no social

pleasures, so they gradually acquired an agreeable circle of friends, who

shared the interests of both wife and husband. Helmholtz’ wife was a faithful

help-meet and true comrade, who worked and wrote for him. He read aloud

to her the lectures he was going to deliver, so that she might judge how they

would appeal to an educated audience. However, her health, which had long

been a cause of concern, steadily grew worse. The doctors thought that the

cold climate of Ko¨ nigsberg was one cause of her frequent illnesses, so, when

the professorship of physiology in Bonn fell vacant, Helmholtz enlisted the

support of von Humboldt in order to have himself transferred there.

Hermann von Helmholtz (1821–1894) 135

In 1855, when he moved to Bonn, Helmholtz’ great treatise, the Handbook

of Physiological Optics, was completed. It was the culmination of five

fruitful years spent in Ko¨ nigsberg, years of prolific academic work and high

achievement in various branches of science. Just before leaving for Bonn, he

received an invitation from William Thomson, the future Lord Kelvin, to

address the forthcoming meeting of the British Association in Hull. On the

way to Hull he passed through London, where he saw Faraday at the Royal

Institution and George Biddell Airy, the Astronomer Royal, at the Royal

Observatory. ‘Faraday is as simple, charming and unaffected as a child’, he

noted, ‘I have never seen a man with such winning ways.’ At the meeting

he was particularly impressed by the fact that his audience of 850 included

236 ladies. ‘Here in England’, he wrote home, ‘the ladies seem to be very

well up in science.’

Helmholtz soon accustomed himself to life in Bonn, where his wife’s

health improved considerably, thanks to the milder climate. Officially his

duties were to teach anatomy, for which he was certainly qualified but felt

the lack of any previous teaching experience. He also lectured on his main

subject of physiology. In his experimental work he was at first handicapped

by the lack of scientific instruments; he had been able to take only very few

of them with him from K¨ onigsberg and he found practically nothing useful

when he arrived at Bonn. His interests were now turning from the theory of

vision to that of sound. He applied the mathematics of Fourier series, which

led to another classic work, the Theory of the Sensations of Tone.

However, Helmholtz had hardly settled down in Bonn when he

received an invitation to move again, this time to Heidelberg, where he

would be appointed professor of physiology, rather than anatomy. Bonn

attempted to retain him by increasing his salary and promising to improve

the facilities provided for anatomy. He and his wife already had made many

good friends in Bonn. Against this, Heidelberg boasted Robert Bunsen and

Gustav Kirchhoff, two of the leading scientists of the period. Although the

state of his wife’s health made another move undesirable, in the end he

decided on Heidelberg. The Prussians, who governed Bonn, made every

effort to dissuade him, but they succeeded only in delaying the transfer

until 1858, when he joined Bunsen and Kirchhoff to inaugurate the most

glorious age in Heidelberg science.

The Helmholtz family, which now included two small children,K¨athe

and Richard, settled down well in Heidelberg. He was elected a corresponding

member of the Academy of Sciences in Munich and attended its festival

in March 1859, meeting some of the other academicians, as well as the

136 From Ohm to Helmholtz

composer Richard Wagner and King Ludwig II. Meanwhile he received the

news from Potsdam that his father, to whom he was closely attached, had

died following a stroke, while at home it was increasingly clear that the

health of his beloved wife was rapidly declining. She died at the end of the

year, leaving him despondent. He was already suffering from migraine and

fainting fits, brought on by the strain. He sought comfort and distraction

in his work. Further recognition came with corresponding membership of

the academies of Vienna and Go¨ ttingen and the award of the Order of the

Golden Lion from the Netherlands.

The subject of the next profile will be Lord Kelvin. When he was

still just William Thompson, he met Helmholtz for the first time when

he was in Germany in 1855. Afterwards Helmholtz wrote to his wife that

‘I expected to find the man, who is one of the first mathematical physicists

of Europe, somewhat older than myself, and was not a little astonished when

a very juvenile and exceedingly fair youth, who looked quite girlish, came

forward . . . he far exceeds all the great men of science with whom I have

made personal acquaintance, in intelligence and lucidity and mobility of

thought, so that I felt quite wooden besides him sometimes.’

A remarkably close friendship and scientific collaboration sprang

up between Helmholtz and Thompson, which lasted until the death of

Helmholtz, nearly forty years later. In the summer of 1860 he went to stay

with Thomson on the Isle of Arran; and the following February wrote to

him about his plans for the future:

I had seriously to think of introducing a new order of things, and if

this had to be done, it was better it should be soon. In the end it came

about more rapidly than I expected, for when love has once obtained

permission to germinate, it grows without further appeal to reason.

My fianc´ee is a gifted maiden, young in comparison with myself, and

is I think one of the beauties of Heidelberg. She is very keen-witted

and intelligent, also accustomed to society, as she received a good deal

of her education in Paris and London . . . I should never have

presumed, as a widower with two children, and no longer in my first

youth, to seek the hand of so young a lady, who had every

qualification for playing a prominent part in society. However it all

came about very quickly and now I can once more face the future

happily. The wedding is to be at Whitsuntide.

Helmholtz’ second wife, Anna von Mohl, was a woman of great force

of character, talented, with wide views and high aspirations, clever in society

Hermann von Helmholtz (1821–1894) 137

and brought up in a circle in which intelligence and character were equally

esteemed. In 1862 a son, Robert Julius, was born, but this nearly cost Anna

her life and the son soon became fatally ill. Then in 1864 she gave birth to

a daughter, Ellen Ada Elizabeth.

At Easter 1861 Helmholtz made another visit to England, to lecture

on the physiological theory of music, and was prevailed upon to give an

evening discourse at the Royal Institution on the application of the law

of the conservation of energy to organic nature. In 1864 he was back in

England for six weeks, mostly in London but also in Oxford, Glasgow and

Manchester: he lectured at the Royal Society and the Royal Institution and

met the young Clerk Maxwell for the first time. The following year he was

in Paris, returning for the Ophthalmological Congress held there during the

Great Exhibition of 1867.

By 1868 Helmholtz had been in Heidelberg for ten years, and the

Prussians decided to make another effort to secure his return. The chair

of physics and mathematics at Bonn had been left vacant by the death

of Julius Plu¨ cker, which led Bonn to enquire whether Helmholtz would

be interested in returning as professor of physics (Plu¨ cker was unusual in

being well-qualified in both disciplines). In his reply Helmholtz explained

that physics had originally been his principal scientific interest and that

he had been led to medicine, particularly physiology, by force of circumstances.

He went on to say that ‘what I have accomplished in physiology

rests mainly upon a physical foundation. The young people whose studies I

now direct are for the most part medical students, and most of them are not

sufficiently grounded in mathematics and physics to take up what I should

consider the best of the subjects that I could teach . . . Lectures in pure

mathematics I could not well undertake; in those on mathematical physics

I should treat mathematics as the means and not as the end.’ Interestingly,

in 1868 he surprised the scientific and mathematical world by publishing an

essay ‘On the Facts that Underlie Geometry’, which had much in common

with Bernhard Riemann’s masterly paper ‘On the Hypotheses that Underlie

Geometry’, published fourteen years earlier, of which he was unaware, but

there were some differences and even errors in Helmholtz’ work.

In the end Helmholtz decided to remain at Heidelberg. Another son,

Friedrich Julius, was born, but did not thrive. At the beginning of 1870

Helmholtz was elected an external member of the Berlin Academy, and

efforts were now made to interest him in moving to the Prussian capital.

The faculty of philosophy at the University of Berlin had a vacancy to fill,

following the death of Magnus, and proposed to offer it to either Kirchhoff

138 From Ohm to Helmholtz

or Helmholtz, with a preference for the former: ‘if Helmholtz is the more

gifted and universal in research, Kirchhoff is the more practised physicist

and successful teacher. While Helmholtz is more productive, and is always

occupied with new problems, Kirchhoff has more inclination to teaching; his

lectures are a model of lucidity and polish; also from what I hear he is better

able to superintend the works of elementary students than Helmholtz.’ By

all accounts Helmholtz was a poor lecturer, who simply read out verbatim

passages from the books he had written. Despite this, he attracted outstanding

students.

When it became clear that Kirchhoff would not leave Heidelberg,

Helmholtz was invited to state his requirements for taking the Berlin post.

Although the university had been founded in 1810, science was not taught

until later and even then only at an elementary level. Helmholtz was determined

to make Berlin a major centre for physics. He asked for an institute

of physics, with the necessary equipment, of which he would be director,

and an official residence. The Minister of Education agreed to his terms

and the Helmholtz family prepared to move. Confirmation of the appointment

was held up until the end of the year, because of the Franco-Prussian

War. Almost immediately afterwards he received a letter from Sir William

Thomson asking whether he would be willing to accept the chair of experimental

physics in Cambridge, but by then Helmholtz felt committed to

Berlin.

Helmholtz and his wife Anna entertained in great style. Their parties

brought together intellectuals, scientists, artists and leaders of both government

and industry. Their daughter Ellen married the son of the great

industrialist Werner von Siemens. The two children by Helmholtz’ first

marriage had been, since his second marriage, in the care of their grandmother.

The daughter K¨athe grew up a serious woman, greatly loved and

admired but never satisfied, a gifted artist who painted in the ateliers of

Berlin and Paris. She spent a year in France and England. After she had

married in 1872 a daughter was born, but then her health declined and she

died five years later. Helmholtz’ eldest son Robert volunteered for military

service and was sent to the front where he was accidentally injured; after

discharge from the army he became a student at the Munich polytechnic

before embarking on a successful career in mechanical engineering.

In 1871 Helmholtz was back in Britain again for the meeting of the

British Association at Edinburgh, meeting beforehand the mathematical

physicist P.G. Tait and the naturalist T.H. Huxley at St Andrews. Later

he joined SirWilliam Thomson, by this time Lord Kelvin, for a cruise on his

yacht. Helmholtz was struck by Kelvin’s easy relationships with students,

Hermann von Helmholtz (1821–1894) 139

engineers, seafarers and aristocrats. The sea was rough, but this was not

allowed to interfere with scientific work.

In 1876, although he had only been there for five years, he was elected

rector of the university; in his inaugural address he particularly praised the

academic freedom enjoyed by German students and faculty, ‘which amazes

all foreigners’. At the end of his year of office he went on a tour of Italy,

seeing various scientists en route, and in 1880 made a similar tour of Spain.

The next year he went to London, accompanied by his wife Anna, to give

the Faraday lecture at the Chemical Society and then on to Cambridge to

receive an honorary degree. In Germany he was elevated to the ranks of the

hereditary nobility and so became entitled to use the prefix ‘von’.

In 1887 he was appointed president of the new physical–technical

institute at Berlin Charlottenburg, which had been established through the

munificence of his friend Werner von Siemens. During the next few years

Helmholtz was much involved in the work of setting up the new institute.

Although he retained his position at the university, he was relieved of many

of the routine duties attached to it. He crossed the Atlantic for the first time

on the occasion of the Chicago World’s Fair; his wife, who went with him,

had serious misgivings about the wisdom of making the journey. They were

impressed by the cities of the east and by Niagara Falls, but not by the

prairies; they went as far west as the Rockies. Felix Klein, who was with

them, wrote an account of what happened on the voyage back to Europe:

‘we were sitting in the smoking room till about 10 p.m. with a perfectly

calm sea . . . when Helmholtz, remarking that it was time to go to bed, went

down a fairly steep stairway leading to the saloon. Then we heard a heavy

fall . . . on which we all hurried below, and were in time to see Helmholtz

lifted by a number of stewards at the foot of the gangway, and carried into

his cabin; there was a pool of blood on the floor.’ His wife Anna, who was

suffering from sickness at the time, wrote to the children:

Professor Klein came in, and broke to me that your father had fallen

down the companion way, and was bleeding from the forehead and

nose, and that two doctors were with him; and he led me into the

ship’s doctor’s cabin. There lay your father covered with blood, but he

appeared to be conscious and was able to answer all questions. At first

they feared an apoplectic stroke, which I never believed for a moment,

but I think one of his old and long-forgotten swoons must have

suddenly come over him. Evidently he had become unconscious before

the fall, since he did not put out his hands to protect himself but fell

heavily on his face.

140 From Ohm to Helmholtz

Helmholtz gradually recovered from the accident, but he was weakened

by it and suffered from double vision and vertigo. There were other

shocks in store; the death of his beloved son Robert, the constant illness in

mind and body of his invalid son Fritz and then the untimely death of his disciple

Heinrich Hertz, a great loss to science. Nevertheless, Helmholtz was

able to carry on both his scientific research and his administrative duties

at the institute until, on July 12, 1894, he experienced a stroke, which left

him confused and partially paralysed. His condition gradually deteriorated

until the end came in his seventy-third year on September 8, 1894. His wife

survived him by five years; their son Fritz died in 1901, at the age of 33.

The enormous influence Helmholtz wielded derived from his magnetic

personality. The notoriously reticent and undemonstrative physicist

Max Planck gives us some idea of how impressive this was:

In his whole personality, his incorruptible judgement and in his

modest manner he represented the dignity and truth of science. I was

deeply touched by his human kindness. When in conversation he

looked at me with his quiet, searching but benevolent eyes, I was

seized by a feeling of boundless, childlike devotion. I would have been

prepared to confide in him anything which affected me deeply in the

certainty of finding in him a just and mild counsellor, and an

appreciative or even praising word from his mouth gave me greater

happiness than all the success I could achieve in this world.