Hermann von Helmholtz

Hermann Ludwig Ferdinand von Helmholtz (August 31, 1821 – September 8, 1894) was a German physician and physicist who made significant contributions in several scientific fields. The largest German association of research institutions, the Helmholtz Association, is named after him.[5]

In physiology and psychology, he is known for his mathematics of the eye, theories of vision, ideas on the visual perception of space, color vision research, and on the sensation of tone, perception of sound, and empiricism in the physiology of perception.

In physics, he is known for his theories on the conservation of energy, work in electrodynamics, chemical thermodynamics, and on a mechanical foundation of thermodynamics.

As a philosopher, he is known for his philosophy of science, ideas on the relation between the laws of perception and the laws of nature, the science of aesthetics, and ideas on the civilizing power of science.

Hermann von Helmholtz

Hermann von Helmholtz
Hermann Ludwig Ferdinand Helmholtz

August 31, 1821
DiedSeptember 8, 1894 (aged 73)
Alma materMedicinisch-chirurgisches Friedrich-Wilhelm-Institut
Known for
Scientific career
ThesisDe fabrica systematis nervosi evertebratorum (1842)
Doctoral advisorJohannes Peter Müller
Doctoral students
Other notable students
InfluencedFriedrich Albert Lange[3]
Ludwig Wittgenstein[4]
Helmholtz's polyphonic siren, Hunterian Museum, Glasgow
Helmholtz's polyphonic siren, Hunterian Museum, Glasgow


Early years

Helmholtz was born in Potsdam the son of the local 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 was influenced by the philosophy of Johann Gottlieb Fichte and Immanuel 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.

Trained primarily in physiology, Helmholtz wrote on many other topics, ranging from theoretical physics, to the age of the Earth, to the origin of the Solar System.

University posts

Helmholtz's first academic position was as a teacher of Anatomy at the Academy of Arts in Berlin in 1848.[6] He then moved to take a post of associate professor of physiology at the Prussian University of Königsberg, where he was appointed in 1849. In 1855 he accepted a full professorship of anatomy and physiology at the University of Bonn. He was not particularly happy in Bonn, however, and three years later he transferred to the University of Heidelberg, in Baden, where he served as professor of physiology. In 1871 he accepted his final university position, as professor of physics at the Humboldt University in Berlin.


Helmholtz 1848
Helmholtz in 1848


His first important scientific achievement, an 1847 treatise on the conservation of energy, was written in the context of his medical studies and philosophical background. His work on energy conservation came about 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, Benoît Paul 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, or energy in today's terminology. He published his theories in his book Über die Erhaltung der Kraft (On the Conservation of Force, 1847).[7]

In the 1850s and 60s, building on the publications of William Thomson, Helmholtz and William Rankine popularized the idea of the heat death of the universe.

In fluid dynamics, Helmholtz made several contributions, including Helmholtz's theorems for vortex dynamics in inviscid fluids.

Sensory physiology

Helmholtz was a pioneer in the scientific study of human vision and audition. Inspired by psychophysics, he was interested in the relationships between measurable physical stimuli and their correspondent human perceptions. For example, the amplitude of a sound wave can be varied, causing the sound to appear louder or softer, but a linear step in sound pressure amplitude does not result in a linear step in perceived loudness. The physical sound needs to be increased exponentially in order for equal steps to seem linear, a fact that is used in current electronic devices to control volume. Helmholtz paved the way in experimental studies on the relationship between the physical energy (physics) and its appreciation (psychology), with the goal in mind to develop "psychophysical laws."

The sensory physiology of Helmholtz was the basis of the work of Wilhelm Wundt, a student of Helmholtz, who is considered one of the founders of experimental psychology. More explicitly than Helmholtz, Wundt described his research as a form of empirical philosophy and as a study of the mind as something separate. Helmholtz had, in his early repudiation of Naturphilosophie, stressed the importance of materialism, and was focusing more on the unity of "mind" and body.[8]

Ophthalmic optics

In 1851, Helmholtz revolutionized the field of ophthalmology with the invention of the ophthalmoscope; an instrument used to examine the inside of the human eye. This made him world-famous overnight. Helmholtz's interests at that time were increasingly focused on the physiology of the senses. His main publication, titled Handbuch der Physiologischen Optik (Handbook of Physiological Optics or Treatise on Physiological Optics), provided empirical theories on depth perception, color vision, and motion perception, and became the fundamental reference work in his field during the second half of the nineteenth century. In the third and final volume, published in 1867, Helmholtz described the importance of unconscious inferences for perception. The Handbuch was first translated into English under the editorship of James P. C. Southall on behalf of the Optical Society of America in 1924-5. His theory of accommodation went unchallenged until the final decade of the 20th century.

Helmholtz continued to work for several decades on several editions of the handbook, frequently updating his work because of his dispute with Ewald Hering who held opposite views on spatial and color vision. This dispute divided the discipline of physiology during the second half of the 1800s.

Nerve physiology

In 1849, while at Königsberg, Helmholtz measured the speed at which the signal is carried along a nerve fibre. At that time most people believed that nerve signals passed along nerves immeasurably fast.[9] He used a recently dissected sciatic nerve of a frog and the calf muscle to which it attached. He used a galvanometer as a sensitive timing device, attaching a mirror to the needle to reflect a light beam across the room to a scale which gave much greater sensitivity.[9] Helmholtz reported[10][11] transmission speeds in the range of 24.6 - 38.4 meters per second.[9]

Acoustics and aesthetics

Helmholtz resonator 2
The Helmholtz resonator (i) and instrumentation

In 1863, Helmholtz published Sensations of Tone, once again demonstrating his interest in the physics of perception. This book influenced musicologists into the twentieth century. Helmholtz invented the Helmholtz resonator to identify the various frequencies or pitches of the pure sine wave components of complex sounds containing multiple tones.[12]

Helmholtz showed that different combinations of resonator could mimic vowel sounds: Alexander Graham Bell in particular was interested in this but, not being able to read German, misconstrued Helmholtz' diagrams as meaning that Helmholtz had transmitted multiple frequencies by wire—which would allow multiplexing of telegraph signals—whereas, in reality, electrical power was used only to keep the resonators in motion. Bell failed to reproduce what he thought Helmholtz had done but later said that, had he been able to read German, he would not have gone on to invent the telephone on the harmonic telegraph principle.[13][14][15][16]

Helmholtz 1876
Helmholtz in 1876
(portrait by Franz von Lenbach)

The translation by Alexander J. Ellis was first published in 1875 (the first English edition was from the 1870 third German edition; Ellis's second English edition from the 1877 fourth German edition was published in 1885; the 1895 and 1912 third and fourth English editions were reprints of the second).[17]


Helmholtz studied the phenomena of electrical oscillations from 1869 to 1871, and in a lecture delivered to the Naturhistorisch-medizinischen Vereins zu Heidelberg (Natural History and Medical Association of Heidelberg) on April 30, 1869, titled On Electrical Oscillations he indicated that the perceptible damped electrical oscillations in a coil joined up with a Leyden jar were about 1/50th of a second in duration.[18]

In 1871, Helmholtz moved from Heidelberg to Berlin to become a professor in physics. He became interested in electromagnetism and the Helmholtz equation is named for him. Although he did not make major contributions to this field, his student Heinrich Rudolf Hertz became famous as the first to demonstrate electromagnetic radiation. Oliver Heaviside criticised Helmholtz's electromagnetic theory because it allowed the existence of longitudinal waves. Based on work on Maxwell's equations, Heaviside pronounced that longitudinal waves could not exist in a vacuum or a homogeneous medium. Heaviside did not note, however, that longitudinal electromagnetic waves can exist at a boundary or in an enclosed space.[19]

There is even a topic by the name "Helmholtz optics", based on the Helmholtz equation.[20][21][22]


Whoever, in the pursuit of science, seeks after immediate practical utility may rest assured that he seeks in vain. — Academic Discourse (Heidelberg 1862)[23]

Students and associates

Other students and research associates of Helmholtz at Berlin included Max Planck, Heinrich Kayser, Eugen Goldstein, Wilhelm Wien, Arthur König, Henry Augustus Rowland, Albert A. Michelson, Wilhelm Wundt, Fernando Sanford and Michael I. Pupin. Leo Koenigsberger, who was his colleague 1869–1871 in Heidelberg, wrote the definitive biography of him in 1902.

Honours and legacy

Hermann von Helmholtz-Statue vor der Humboldt-Universität zu Berlin
Helmholtz's statue in front of Humboldt University in Berlin

Decree awarding Helmholtz (listed in first page) the French Legion of Honour

French Presidential Decree -Award of Legion of Honour to Helholtz, Bell and Edison -10 November 1881 Pg. 1
French Presidential Decree -Award of Legion of Honour to Helholtz, Bell and Edison -10 November 1881 Pg. 3
French Presidential Decree -Award of Legion of Honour to Helholtz, Bell and Edison -10 November 1881 Pg. 5


  • On the Conservation of Force (1847) HathiTrust
  • Helmholtz, Herman (1876). "On the Limits of the Optical Capacity of the Microscope". Monthly Microscopical Journal. 16: 15–39. doi:10.1111/j.1365-2818.1876.tb05606.x.
  • On the Conservation of Force (1895) Introduction to a Series of Lectures Delivered at Carlsruhe in the Winter of 1862–1863, English translation
  • On the Sensations of Tone as a Physiological Basis for the Theory of Music (downloadable from California Digital Library) Third Edition of English Translation, based on Fourth German Edition of 1877, By Hermann von Helmholtz, Alexander John Ellis, Published by Longmans, Green, 1895, 576 pages
  • On the Sensations of Tone as a Physiological Basis for the Theory of Music (downloadable from Google Books) Fourth Edition, By Hermann von Helmholtz, Alexander John Ellis, Published by Longmans, Green, 1912, 575 pages
  • Treatise on Physiological Optics (1910) three volumes. English translation by Optical Society of America (1924–5).
  • Popular lectures on scientific subjects (1885)
  • Popular lectures on scientific subjects second series (1908)

See also



  1. ^ David Cahan (1993). Hermann Von Helmholtz and the Foundations of Nineteenth-Century Science. University of California Press. p. 198. ISBN 978-0-520-08334-9.
  2. ^ Hermann von Helmholtz entry at the Stanford Encyclopedia of Philosophy by Lydia Patton
  3. ^ Friedrich Albert Lange entry at the Stanford Encyclopedia of Philosophy by Nadeem J. Z. Hussain
  4. ^ Patton, Lydia, 2009, "Signs, Toy Models, and the A Priori: from Helmholtz to Wittgenstein," Studies in the History and Philosophy of Science, 40 (3): 281–289.
  5. ^ a b Cahan, David (1993). Hermann von Helmholtz and the Foundations of Nineteenth-Century Science. University of California Press. ISBN 978-0-520-08334-9.
  6. ^ Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002 (PDF). The Royal Society of Edinburgh. July 2006. ISBN 0 902 198 84 X.
  7. ^ English translation published in Scientific memoirs, selected from the transactions of foreign academies of science, and from foreign journals: Natural philosophy (1853), p. 114; trans. by John Tyndall. Google Books, HathiTrust
  8. ^ Peter J. Bowler and Iwan Rhys Morus (2005). Making Modern Science: A Historical Survey. University of Chicago Press. p. 177. ISBN 978-0-226-06861-9.
  9. ^ a b c Glynn, Ian (2010). Elegance in Science. Oxford: Oxford University Press. pp. 147–150. ISBN 978-0-19-957862-7.
  10. ^ Vorläufiger Bericht über die Fortpflanzungs-Geschwindigkeit der Nervenreizung. In: Archiv für Anatomie, Physiologie und wissenschaftliche Medicin. Jg. 1850, Veit & Comp., Berlin 1850, S. 71-73. MPIWG Berlin
  11. ^ Messungen über den zeitlichen Verlauf der Zuckung animalischer Muskeln und die Fortpflanzungsgeschwindigkeit der Reizung in den Nerven. In: Archiv für Anatomie, Physiologie und wissenschaftliche Medicin. Jg. 1850, Veit & Comp., Berlin 1850, S. 276-364. MPIWG Berlin
  12. ^ Helmholtz, Hermann von (1885), On the sensations of tone as a physiological basis for the theory of music, Second English Edition, translated by Alexander J. Ellis. London: Longmans, Green, and Co., p. 44. Retrieved 2010-10-12.
  13. ^ "PBS, American Experience: The Telephone -- More About Bell".
  14. ^ MacKenzie 2003, p. 41.
  15. ^ Groundwater 2005, p. 31.
  16. ^ Shulman 2008, pp. 46–48.
  17. ^ Hermann L. F. Helmholtz, M.D. (1912). On the Sensations of Tone as a Physiological Basis for the Theory of Music (Fourth ed.). Longmans, Green, and Co.
  18. ^ Koenigsberger, Leo (28 March 2018). "Hermann von Helmholtz". Clarendon press. Retrieved 28 March 2018 – via Google Books.
  19. ^ John D. Jackson, Classical Electrodynamics, ISBN 0-471-30932-X.
  20. ^ Kurt Bernardo Wolf and Evgenii V. Kurmyshev, Squeezed states in Helmholtz optics, Physical Review A 47, 3365–3370 (1993).
  21. ^ Sameen Ahmed Khan, Wavelength-dependent modifications in Helmholtz Optics, International Journal of Theoretical Physics, 44(1), 95-125 (January 2005).
  22. ^ Sameen Ahmed Khan, A Profile of Hermann von Helmholtz, Optics & Photonics News, Vol. 21, No. 7, pp. 7 (July/August 2010).
  23. ^ "Science". Moses King. 28 March 2018. Retrieved 28 March 2018 – via Google Books.
  24. ^ "Honorary Fellows of the Royal College of Surgeons (RCSI) since 1784". Ireland Genealogy Project. 2013.
  25. ^ "Honorary Members and Fellows". The Institution of Engineers and Shipbuilders in Scotland.
  26. ^ "History of the name in the About section of Helmholtz Association website". Archived from the original on 14 April 2012. Retrieved 30 April 2012.
  27. ^ "11573 Helmholtz (1993 SK3)". Minor Planet Center. Retrieved 2 February 2018.
  28. ^ "Lunar crater Helmholtz". Gazetteer of Planetary Nomenclature. USGS Astrogeology Research Program.
  29. ^ "Martian crater Helmholtz". Gazetteer of Planetary Nomenclature. USGS Astrogeology Research Program.
  30. ^ "Helmholtzstraße". berlin.de. Retrieved 18 July 2018.


  • Cahan, David Helmholtz: A Life in Science. University of Chicago Press, 2018. ISBN 978-0-226-48114-2.
  • Cohen, Robert, and Wartofsky, Marx, eds. and trans. Reidel. Helmholtz: Epistemological Writings, 1977.
  • Ewald, William B., ed. From Kant to Hilbert: A Source Book in the Foundations of Mathematics, 2 vols. Oxford Uni. Press, 1996.
    • 1876. "The origin and meaning of geometrical axioms," 663–88.
    • 1878. "The facts in perception," 698–726.
    • 1887. "Numbering and measuring from an epistemological viewpoint," 727–52.
  • Groundwater, Jennifer. Alexander Graham Bell: The Spirit of Invention. Calgary: Altitude Publishing, 2005. ISBN 1-55439-006-0.
  • Jackson, Myles W. Harmonious Triads: Physicists, Musicians, and Instrument Makers in Nineteenth-Century Germany (MIT Press, 2006).
  • Kahl, Russell, ed. Wesleyan. Selected Writings of Hermann von Helmholtz, Uni. Press., 1971.
  • Koenigsberger, Leo. Hermann von Helmholtz, translated by Frances A. Welby (Dover, 1965)
  • MacKenzie, Catherine. Alexander Graham Bell. Whitefish, Montana: Kessinger Publishing, 2003. ISBN 978-0-7661-4385-2. Retrieved July 29, 2009.
  • Shulman, Seth. The Telephone Gambit: Chasing Alexander Bell's Secret. New York: Norton & Company, 2008. ISBN 978-0-393-06206-9.

Further reading

  • David Cahan: Helmholtz: A Life in Science (University of Chicago, 2018). ISBN 978-0-226-48114-2
  • David Cahan (Ed.): Hermann von Helmholtz and the Foundations of Nineteenth-Century Science. Univ. California, Berkeley 1994, ISBN 978-0-520-08334-9.
  • Gregor Schiemann: Hermann von Helmholtz's Mechanism: The Loss of Certainty. A Study on the Transition from Classical to Modern Philosophy of Nature. Dordrecht: Springer 2009, ISBN 978-1-4020-5629-1.
  • Franz Werner: Hermann Helmholtz´ Heidelberger Jahre (1858–1871). (= Sonderveröffentlichungen des Stadtarchivs Heidelberg 8). Mit 52 Abbildungen. Berlin / Heidelberg (Springer) 1997.

External links

Gibbs–Helmholtz equation

The Gibbs–Helmholtz equation is a thermodynamic equation used for calculating changes in the Gibbs energy of a system as a function of temperature. It is named after Josiah Willard Gibbs and Hermann von Helmholtz.


The equation is:

where H is the enthalpy, T the absolute temperature and G the Gibbs free energy of the system, all at constant pressure p. The equation states that the change in the G/T ratio at constant pressure as a result of an infinitesimally small change in temperature is a factor H/T2.

Helmholtz's theorems

In fluid mechanics, Helmholtz's theorems, named after Hermann von Helmholtz, describe the three-dimensional motion of fluid in the vicinity of vortex filaments. These theorems apply to inviscid flows and flows where the influence of viscous forces are small and can be ignored.

Helmholtz's three theorems are as follows:

Helmholtz's first theorem

The strength of a vortex filament is constant along its length.

Helmholtz's second theorem

A vortex filament cannot end in a fluid; it must extend to the boundaries of the fluid or form a closed path.

Helmholtz's third theorem

In the absence of rotational external forces, a fluid that is initially irrotational remains irrotational.Helmholtz's theorems apply to inviscid flows. In observations of vortices in real fluids the strength of the vortices always decays gradually due to the dissipative effect of viscous forces.

Alternative expressions of the three theorems are as follows:

1. The strength of a vortex tube does not vary with time.

2. Fluid elements lying on a vortex line at some instant continue to lie on that vortex line. More simply, vortex lines move with the fluid. Also vortex lines and tubes must appear as a closed loop, extend to infinity or start/end at solid boundaries.

3. Fluid elements initially free of vorticity remain free of vorticity.

Helmholtz's theorems have application in understanding:

Generation of lift on an airfoil

Starting vortex

Horseshoe vortex

Wingtip vortices.Helmholtz's theorems are now generally proven with reference to Kelvin's circulation theorem. However the Helmholtz's theorems were published in 1858, nine years before the 1867 publication of Kelvin's theorem. There was much communication between the two men on the subject of vortex lines, with many references to the application of their theorems to the study of smoke rings.

Helmholtz (Martian crater)

Helmholtz Crater is an impact crater in the Argyre quadrangle on Mars at 45.8°S and 21.3°W and is 111.5 km in diameter. Helmholtz is located just east of Argyre Planitia. Its name refers to German physicist Hermann von Helmholtz (1821–1894).

Helmholtz (lunar crater)

Helmholtz is a lunar impact crater, approximately 110 kilometers in diameter, that is located near the south-southeast limb of the Moon. Attached to the south-southeast rim of Helmholtz is the somewhat smaller crater Neumayer. The larger crater Boussingault is nearly attached to the west-southwestern rim.

Helmholtz Association of German Research Centres

The Helmholtz Association of German Research Centres (German: Helmholtz-Gemeinschaft Deutscher Forschungszentren) is the largest scientific organisation in Germany. It is a union of 18 scientific-technical and biological-medical research centers. The official mission of the Association is "solving the grand challenges of science, society and industry". Scientists at Helmholtz therefore focus research on complex systems which affect human life and the environment. The namesake of the association is the German physiologist and physicist Hermann von Helmholtz.The annual budget of the Helmholtz Association amounts to €4.4 billion, of which about 70% is raised from public funds. The remaining 30% of the budget is acquired by the 19 individual Helmholtz Centres in the form of contract funding. The public funds are provided by the federal government (90%) and the rest by the States of Germany (10%).

Helmholtz coil

A Helmholtz coil is a device for producing a region of nearly uniform magnetic field, named after the German physicist Hermann von Helmholtz. It consists of two electromagnets on the same axis. Besides creating magnetic fields, Helmholtz coils are also used in scientific apparatus to cancel external magnetic fields, such as the Earth's magnetic field.

Helmholtz decomposition

In physics and mathematics, in the area of vector calculus, Helmholtz's theorem, also known as the fundamental theorem of vector calculus, states that any sufficiently smooth, rapidly decaying vector field in three dimensions can be resolved into the sum of an irrotational (curl-free) vector field and a solenoidal (divergence-free) vector field; this is known as the Helmholtz decomposition or Helmholtz representation. It is named after Hermann von Helmholtz.

As an irrotational vector field has a scalar potential and a solenoidal vector field has a vector potential, the Helmholtz decomposition states that a vector field (satisfying appropriate smoothness and decay conditions) can be decomposed as the sum of the form , where Φ is a scalar field, called scalar potential, and A is a vector field, called a vector potential.

Helmholtz equation

In mathematics and physics, the Helmholtz equation, named for Hermann von Helmholtz, is the linear partial differential equation

where is the Laplacian, is the wave number, and is the amplitude. This is also an eigenvalue equation.

Helmholtz machine

The Helmholtz machine is a type of artificial neural network that can account for the hidden structure of a set of data by being trained to create a generative model of the original set of data. The hope is that by learning economical representations of the data, the underlying structure of the generative model should reasonably approximate the hidden structure of the data set. A Helmholtz machine contains two networks, a bottom-up recognition network that takes the data as input and produces a distribution over hidden variables, and a top-down "generative" network that generates values of the hidden variables and the data itself.

Helmholtz machines are usually trained using an unsupervised learning algorithm, such as the wake-sleep algorithm.Helmholtz machines may also be used in applications requiring a supervised learning algorithm (e.g. character recognition, or position-invariant recognition of an object within a field).

Helmholtz pitch notation

Helmholtz pitch notation is a system for naming musical notes of the Western chromatic scale. Developed by the German scientist Hermann von Helmholtz, it uses a combination of upper and lower case letters (A to G), and the sub- and super-prime symbols ( ͵  ′ ) to describe each individual note of the scale. It is one of two formal systems for naming notes in a particular octave, the other being scientific pitch notation.

Helmholtz resonance

Helmholtz resonance or wind throb is the phenomenon of air resonance in a cavity, such as when one blows across the top of an empty bottle. The name comes from a device created in the 1850s by Hermann von Helmholtz, the Helmholtz resonator, which he used to identify the various frequencies or musical pitches present in music and other complex sounds.

Helmholtz theorem (classical mechanics)

The Helmholtz theorem of classical mechanics reads as follows:


be the Hamiltonian of a one-dimensional system, where

is the kinetic energy and

is a "U-shaped" potential energy profile which depends on a parameter . Let denote the time average. Let


Kelvin–Helmholtz instability

The Kelvin–Helmholtz instability (after Lord Kelvin and Hermann von Helmholtz) can occur when there is velocity shear in a single continuous fluid, or where there is a velocity difference across the interface between two fluids. An example is wind blowing over water: The instability manifests in waves on the water surface. More generally, clouds, the ocean, Saturn's bands, Jupiter's Red Spot, and the sun's corona show this instability.

Kelvin–Helmholtz mechanism

The Kelvin–Helmholtz mechanism is an astronomical process that occurs when the surface of a star or a planet cools. The cooling causes the pressure to drop, and the star or planet shrinks as a result. This compression, in turn, heats the core of the star/planet. This mechanism is evident on Jupiter and Saturn and on brown dwarfs whose central temperatures are not high enough to undergo nuclear fusion. It is estimated that Jupiter radiates more energy through this mechanism than it receives from the Sun, but Saturn might not. The latter process causes Jupiter to shrink at a rate of two centimetres each year.The mechanism was originally proposed by Kelvin and Helmholtz in the late nineteenth century to explain the source of energy of the Sun. By the mid-nineteenth century, conservation of energy had been accepted, and one consequence of this law of physics is that the Sun must have some energy source to continue to shine. Because nuclear reactions were unknown, the main candidate for the source of solar energy was gravitational contraction.

However, it soon was recognized by Sir Arthur Eddington and others that the total amount of energy available through this mechanism only allowed the Sun to shine for millions of years rather than the billions of years that the geological and biological evidence suggested for the age of the Earth. (Kelvin himself had argued that the Earth was millions, not billions, of years old.) The true source of the Sun's energy remained uncertain until the 1930s, when it was shown by Hans Bethe to be nuclear fusion.


A keratometer, also known as an ophthalmometer, is a diagnostic instrument for measuring the curvature of the anterior surface of the cornea, particularly for assessing the extent and axis of astigmatism. It was invented by the German physiologist Hermann von Helmholtz in 1851, although an earlier model was developed in 1796 by Jesse Ramsden and Everard Home.

A keratometer uses the relationship between object size (O), image size (I), the distance between the reflective surface and the object (d), and the radius of the reflective surface (R). If three of these variables are known (or fixed), the fourth can be calculated using the formula

There are two distinct variants of determining R; Javal-Schiotz type keratometers have a fixed image size and are typically 'two position', whereas Bausch and Lomb type keratometers have a fixed object size and are usually 'one position'.

List of things named after Hermann von Helmholtz

Hermann von Helmholtz (1821 – 1894), German physician and physicist who made significant contributions to several widely varied areas of modern science, is the eponym of the topics listed below.

Statue of Hermann von Helmholtz

The statue of Hermann von Helmholtz by Ernst Herter is located at Humboldt University of Berlin in Berlin-Mitte, Germany.


In thermodynamics, a thermodynamicist is someone who studies thermodynamic processes and phenomena, i.e. the physics that deal with mechanical action and relations of heat.

Among the well-known number of famous thermodynamicists, include Sadi Carnot, Rudolf Clausius, Willard Gibbs, Hermann von Helmholtz, and Max Planck.

Young–Helmholtz theory

The Young–Helmholtz theory (based on the work of Thomas Young and Hermann von Helmholtz in the 19th century), also known as the Trichromatic Theory, is a theory of trichromatic color vision – the manner in which the photoreceptor cells in the eyes of humans and other primates work to enable color vision. In 1802, Young postulated the existence of three types of photoreceptors (now known as cone cells) in the eye, each of which was sensitive to a particular range of visible light.Hermann von Helmholtz developed the theory further in 1850: that the three types of cone photoreceptors could be classified as short-preferring (blue), middle-preferring (green), and long-preferring (red), according to their response to the wavelengths of light striking the retina. The relative strengths of the signals detected by the three types of cones are interpreted by the brain as a visible color.

For instance, yellow light uses different proportions of red and green, but little blue, so any hue depends on a mix of all three cones, for example, a strong blue, medium green, and low red. Moreover, the intensity of colors can be changed without changing their hues, since intensity depends on the frequency of discharge to the brain, as a blue-green can be brightened but retain the same hue. The system is not perfect, as it does not distinguish yellow from a red-green mixture, but can powerfully detect subtle environmental changes.

The existence of cells sensitive to three different wavelength ranges (most sensitive to yellowish green, cyanish-green, and blue – not red, green and blue) was first shown in 1956 by Gunnar Svaetichin. In 1983 it was validated in human retinas in an experiment by Dartnall, Bowmaker, and Mollon, who obtained microspectrophotopic readings of single eye cone cells. Earlier evidence for the theory had been obtained by looking at light reflected from the retinas of living humans, and absorption of light by retinal cells removed from corpses.

Copley Medallists (1851–1900)

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