Hermann Ludwig Ferdinand von Helmholtz
Born August 31, 1821
Died September 8, 1894
Charlottenburg, Berlin, Germany
Field Physicist and physiologist
for Conservation of energy
Hermann Ludwig Ferdinand von Helmholtz (August 31, 1821 – September
8, 1894) was a German physician and physicist. In the words of the 1911
Britannica, "his life from first to last was one of devotion to
science, and he must be accounted, on intellectual grounds, as one of
the foremost men of the 19th century."
Helmholtz was the son of the Potsdam Gymnasium headmaster, Ferdinand
Helmholtz, who had studied classical philology and philosophy, and who
was a close friend of the publisher and philosopher Immanuel Hermann
Fichte. Helmholtz's work is influenced by the philosophy of Fichte and
Kant. He tried to trace their theories in empirical matters like physiology.
As a young man,
Helmholtz was interested in natural science, but his father wanted him
to study medicine at the Charité because there was financial
support for medical students.
about many topics ranging from the age of the Earth to the origin of
the solar system.
To understand the significance of Helmholtz's work in the context of
the development of thermodynamics, see Thermodynamics timeline
His first important
scientific achievement, an 1847 physics treatise on the conservation
of energy was written in the context of his medical studies and philosophical
background. He discovered the principle of conservation of energy while
studying muscle metabolism. He tried to demonstrate that no energy is
lost in muscle movement, motivated by the implication that there were
no vital forces necessary to move a muscle. This was a rejection of
the speculative tradition of Naturphilosophie which was at that time
a dominant philosophical paradigm in German physiology.
Drawing on the earlier
work of Sadi Carnot, Émile Clapeyron and James Prescott Joule,
he postulated a relationship between mechanics, heat, light, electricity
and magnetism by treating them all as manifestations of a single force
(energy in modern terms). He published his theories in his book Über
die Erhaltung der Kraft (On the Conservation of Force, 1847).
Helmholtz is thought
to be the first person to put forward the idea of the heat death of
the universe in 1854.
Born: 31 Aug 1821
in Potsdam, Germany
Died: 8 Sept 1894 in Berlin, Germany
Hermann von Helmholtz's
father was August Ferdinand Julius Helmholtz while his mother was Caroline
Penn. Hermann was the eldest of his parents four children. His childhood
had a strong influence on both his character and his later career. In
particular the views on philosophy held by his father restricted Helmholtz's
had served in the Prussian army in the fight against Napoleon. Despite
having a good university education in philology and philosophy, he became
a teacher at Potsdam Gymnasium. It was a poorly paid job and Hermann
was brought up in financially difficult circumstances. Ferdinand was
an artistic man and his influence meant that Hermann grew up to have
a strong love of music and painting. Caroline Helmholtz was the daughter
of an artillery officer. From her Hermann inherited :-
... the placidity
and reserve which marked his character in later life.
Potsdam Gymnasium where his father taught philology and classical literature.
His interests at school were mainly in physics and he would have liked
to have studied that subject at university. The financial position of
the family, however, meant that he could only study at university if
he received a scholarship. Such financial support was only available
for particular topics and Hermann's father persuaded him that he should
study medicine which was supported by the government.
In 1837 Helmholtz
was awarded a government grant to enable him to study medicine at the
Royal Friedrich-Wilhelm Institute of Medicine and Surgery in Berlin.
He did not receive the money without strings attached, however, and
he had to sign a document promising to work for ten years as a doctor
in the Prussian army after graduating. In 1838 he began his studies
in Berlin. Although he was officially studying at the Institute of Medicine
and Surgery, being in Berlin he had the opportunity of attending courses
at the University. He took this chance, attending lectures in chemistry
contributions to mathematics later in his career it would be reasonable
to have expected him to have taken mathematics courses at the University
of Berlin at this time. However he did not, rather he studied mathematics
on his own, reading works by Laplace, Biot and Daniel Bernoulli. He
also read philosophy works at this time, particularly the works of Kant.
His research career began in 1841 when he began work on his dissertation.
He rejected the direction which physiology had been taking which had
been based on vital forces which were not physical in nature. Helmholtz
strongly argued for founding physiology completely on the principles
of physics and chemistry.
from the Medical Institute in Berlin in 1843 and was assigned to a military
regiment at Potsdam, but spent all his spare time doing research. His
work still concentrated, as we remarked above, on showing that muscle
force was derived from chemical and physical principles. If some vital
force were present, he argued, then perpetual motion would become possible.
In 1847 he published his ideas in a very important paper Über die
Erhaltung der Kraft which studied the mathematical principles behind
the conservation of energy.
in favour of the conservation of energy using both philosophical arguments
and physical arguments. He based many ideas on the earlier works by
Sadi Carnot, Clapeyron, Joule and others. That philosophical arguments
came right up front in this work was typical of all of Helmholtz's contributions.
He argued that physical scientists had to conduct experiments to find
general laws. Then theoretical argument (quoting from the paper):-
... endeavours to
ascertain the unknown causes of processes from their visible effects;
it seeks to comprehend them according to the laws of causality. ...
Theoretical natural science must, therefore, if it is not to rest content
with a partial view of the nature of things, take a position in harmony
with the present conception of the nature of simple forces and the consequences
of this conception. Its task will be completed when the reduction of
phenomena to simple forces is completed, and when it can at the same
time be proved that the reduction given is the only one possible which
the phenomena will permit.
He showed that the
assumption that work could not continually be produced from nothing
led to the conservation of kinetic energy. This principle he then applied
to a variety of different situations. He demonstrated that in various
situations where energy appears to be lost, it is in fact converted
into heat energy. This happens in collisions, expanding gases, muscle
contraction, and other situations. The paper looks at a broad number
of applications including electrostatics, galvanic phenomena and electrodynamics.
The paper is an
important contribution and it was quickly seen as such. In fact it played
a large role in Helmholtz's career for the following year he was released
from his obligation to serve as an army doctor so that he could accept
the vacant chair of physiology at Königsberg. He married Olga von
Velten on 26 August 1849 and settled down to an academic career.
On one hand his
career progressed rapidly in Königsberg. He published important
work on physiological optics and physiological acoustics. He received
great acclaim for his invention of the ophthalmoscope in 1851 and rapidly
gained a strong international reputation. In 1852 he published important
work on physiological optics with his theory of colour vision. However,
experiments which he carried out at this time led him to reject Newton's
theory of colour. The paper was rightly criticised by Grassmann and
Maxwell. Helmholtz was always prepared to admit his mistakes and indeed
he did just this three years later when he published new experimental
results showing those of his 1852 paper to be incorrect.
A visit to Britain
in 1853 saw him form an important friendship with William Thomson. However,
on the other hand, there were problems in Königsberg. Franz Neumann,
the professor of physics in Königsberg was involved in disputes
concerning priority with Helmholtz and the cold weather in Königsberg
had a bad effect on his wife's delicate health. He requested a move
and, in 1855, was appointed to the vacant chair of anatomy and physiology
In 1856 he published
the first volume of his Handbook of physiological optics, then in 1858
he published his important paper in Crelle's Journal on the motion of
a perfect fluid. Helmholtz's paper Über Integrale der hydrodynamischen
Gleichungen, welche den Wirbelbewegungen entsprechen began by decomposing
the motion of a perfect fluid into translation, rotation and deformation.
Helmholtz defined vortex lines as lines coinciding with the local direction
of the axis of rotation of the fluid, and vortex tubes as bundles of
vortex lines through an infinitesimal element of area. Helmholtz showed
that the vortex tubes had to close up and also that the particles in
a vortex tube at any given instant would remain in the tube indefinitely
so no matter how much the tube was distorted it would retain its shape.
Helmholtz was aware
of the topological ideas in his paper, particularly the fact that the
region outside a vortex tube was multiply connected which led him to
consider many-valued potential functions. He described his theoretical
conclusions regarding two circular vortex rings with a common axis of
symmetry in the following way:-
If they both have
the same direction of rotation they will proceed in the same sense,
and the ring in front will enlarge itself and move slower, while the
second one will shrink and move faster, if the velocities of translation
are not too different, the second will finally reach the first and pass
through it. Then the same game will be repeated with the other ring,
so the ring will pass alternately one through the other.
This paper, highly
rigorous in its mathematical approach, did not attract much attention
at the time but its impact on the future work by Tait and Thomson was
very marked. For details of the impact of this work, particularly Helmholtz's
results on vortices, see the article Topology and Scottish mathematical
Before the publication
of this paper Helmholtz had become unhappy with his new position in
Bonn. Part of the problem seemed to revolve round the fact that the
chair involved anatomy and complaints were made to the Minister of Education
that his lectures on this topic were incompetent. Helmholtz reacted
strongly to these criticisms which, he felt, were made by traditionalists
who did not understand his new mechanical approach to the subject. It
was a somewhat strange position for Helmholtz to be in for he had a
very strong reputation as a leading world scientist. When he was offered
the chair in Heidelberg in 1857, he did not accept at once however.
When further sweeteners were put forward in 1858 to entice him to accept,
such as the promise of setting up a new Physiology Institute, Helmholtz
some personal problems. His father died in 1858, then at the end of
1859 his wife, whose health had never been good, died. He was left to
bring up two young children and within eighteen months he married again.
On 16 May 1861 Helmholtz married Anna von Mohl, the daughter of another
professor at Heidelberg :-
Anna, by whom Helmholtz
later had three children, was an attractive, sophisticated woman considerably
younger than her husband. The marriage opened a period of broader social
contacts for Helmholtz.
Some of his most
important work was carried out while he held this post in Heidelberg.
He studied mathematical physics and acoustics producing a major study
in 1862 which looked at musical theory and the perception of sound.
In mathematical appendices he advocated the use of Fourier series. In
1843 Ohm had stated the fundamental principle of physiological acoustics,
concerned with the way in which one hears combination tones. Helmholtz
explained the origin of music on the basis of his fundamental physiological
hypotheses. He formulated a resonance theory of hearing which provided
a physiological explanation of Ohm's principle. His contributions to
the theory of music are discussed fully in .
From around 1866
Helmholtz began to move away from physiology and move more towards physics.
When the chair of physics in Berlin became vacant in 1870 he indicated
his interest in the position. Kirchhoff was the other main candidate
and because he was considered a superior teacher to Helmholtz he was
offered the post. However, when Kirchhoff decided not to accept Helmholtz
was in a strong position. He was able to negotiate a high salary as
well as having Prussia agree to build a new physics institute under
Helmholtz control in Berlin. In 1871 he took up this post.
Helmholtz had begun
to investigate the properties of non-Euclidean space around the time
his interests were turning towards physics in 1867. Bernardo in 
In the second half
of the 19th century, scientists and philosophers were involved in a
heated discussion on the principles of geometry and on the validity
of so-called non-Euclidean geometry. ... Helmholtz's research on the
subject began between 1867 and 1868. Moving from the observation that
our geometric faculties depend on the existence, in nature, of rigid
bodies, he presumed he had given a proof that Euclidean geometry was
the only one compatible with these bodies, maintaining, at the same
time, the empirical, not a priori, origin of geometry. In 1869, after
Beltrami's letter ... he realized he had made a mistake: the empirical
concept of a rigid body and mathematics alone were not enough to characterize
Euclidean geometry. The following year, fully sharing the mathematical
itinerary that, through Gauss, Riemann, Lobachevsky and Beltrami, led
to the creation of the new geometry, he proposed to spread this knowledge
among philosophers while at the same time criticizing the Kantian system.
This marked the beginning of a heated philosophical discussion that
led Helmholtz in 1878 to try to appease the criticisms of the Kantian
A major topic which
occupied Helmholtz after his appointment to Berlin was electrodynamics.
He discussed with Weber the compatibility of Weber's electrodynamics
with the principle of the conservation of energy. In fact the argument
was heated and lasted throughout the 1870s. It was an argument which
neither really won and the 1880s saw Maxwell's theory accepted. Helmholtz
attempted to give a mechanical foundation to thermodynamics, and he
also tried to derive Maxwell's electromagnetic field equations from
the least action principle.
R Steven Turner
writes in :-
his life to seeking the great unifying principles underlying nature.
His career began with one such principle, that of energy, and concluded
with another, that of least action. No less than the idealistic generation
before him, he longed to understand the ultimate, subjective sources
of knowledge. That longing found expression in his determination to
understand the role of the sense organs, as mediators of experience,
in the synthesis of knowledge.
To this continuity
with the past Helmholtz and his generation brought two new elements,
a profound distaste for metaphysics and an undeviating reliance on mathematics
and mechanism. Helmholtz owed the scope and depth characteristic of
his greatest work largely to the mathematical and experimental expertise
which he brought to science. ... Helmholtz was the last great scholar
whose work, in the tradition of Leibniz, embraced all the sciences,
as well as philosophy and the fine arts.