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Heinrich Hertz

From Wikipedia, the free encyclopedia
German physicist (1857–1894)

Heinrich Hertz
Hertz,c. 1890
Born
Heinrich Rudolf Hertz

(1857-02-22)22 February 1857
Died1 January 1894(1894-01-01) (aged 36)
Resting placeOhlsdorf Cemetery, Hamburg
EducationJohanneum Gymnasium
Alma mater
Known for
Spouse
Elisabeth Doll
(m. 1886)
Children2, includingMathilde
FatherGustav Ferdinand Hertz
RelativesGustav Ludwig Hertz (nephew)
Awards
Scientific career
Fields
Institutions
ThesisÜber die Induction in rotirenden Kugeln (On induction in rotating spheres) (1880)
Doctoral advisorHermann von Helmholtz
Other academic advisors
Notable students
Signature

Heinrich Rudolf Hertz (/hɜːrts/hurts;[3]German:[hɛʁts];[4][5] 22 February 1857 – 1 January 1894) was a Germanphysicist who first conclusively proved the existence of theelectromagnetic waves proposed byJames Clerk Maxwell'sequations of electromagnetism.

Biography

[edit]

Heinrich Rudolf Hertz was born on 22 February 1857 inHamburg, the son ofGustav Ferdinand Hertz, a lawyer and politician, and Anna Elisabeth Pfefferkorn.[6][7]

While studying at theGelehrtenschule des Johanneums in Hamburg, Hertz showed an aptitude for sciences as well as languages, learningArabic. He studied sciences and engineering in the German cities ofDresden,Munich, andBerlin, where he studied underGustav Kirchhoff andHermann von Helmholtz. In 1880, Hertz obtained hisPh.D. from theUniversity of Berlin, and for the next three years remained for post-doctoral study under Helmholtz, serving as his assistant. In 1883, Hertz took a post as a lecturer intheoretical physics at theUniversity of Kiel. In 1885, Hertz became a full professor at theUniversity of Karlsruhe.[8]

In 1886, Hertz married Elisabeth Doll, the daughter of Max Doll, a lecturer in geometry at Karlsruhe. They had two daughters: Johanna, born on 20 October 1887 andMathilde, born on 14 January 1891, who went on to become a notable biologist. During this time Hertz conducted his landmark research into electromagnetic waves.[9]

Hertz took a position of Professor of Physics and Director of the Physics Institute at theUniversity of Bonn on 3 April 1889, a position he held until his death. During this time he worked ontheoretical mechanics with his work published in the bookDie Prinzipien der Mechanik in neuem Zusammenhange dargestellt (The Principles of Mechanics Presented in a New Form), published posthumously in 1894.[10]

Death

[edit]

In 1892, Hertz was diagnosed with an infection (after a bout of severemigraines) and underwent operations to treat the illness. He died due to complications after surgery which had attempted to cure his condition. Some consider his ailment to have been caused by a malignant bone condition.[11] He died on 1 January 1894 inBonn, aged 36, and is buried in theOhlsdorf Cemetery in Hamburg.[12][13][14]

Hertz's wife, Elisabeth Hertz (née Doll; 1864–1941), did not remarry. He was survived by his daughters, Johanna (1887–1967) and Mathilde (1891–1975).[15] Neither ever married or had children, hence Hertz has no living descendants.[16]

Scientific work

[edit]

Electromagnetic waves

[edit]
Hertz's 1887 apparatus for generating and detecting radio waves: aspark-gap transmitter(left) consisting of adipole antenna with a spark gap(S) powered by high voltage pulses from aRuhmkorff coil(T), and a receiver(right) consisting of a loop antenna and spark gap.
One of Hertz's radio wave receivers: a loop antenna with an adjustablespark micrometer(bottom).[17]

In 1864 Scottish mathematical physicistJames Clerk Maxwell proposed a comprehensive theory of electromagnetism, now calledMaxwell's equations. Maxwell's theory predicted that coupledelectric andmagnetic fields could travel through space as an "electromagnetic wave". Maxwell proposed that light consisted of electromagnetic waves of short wavelength, but no one had been able to prove this, or generate or detect electromagnetic waves of other wavelengths.[18]

During Hertz's studies in 1879 Helmholtz suggested that Hertz's doctoral dissertation be on testing Maxwell's theory. Helmholtz had also proposed the "Berlin Prize" problem that year at thePrussian Academy of Sciences for anyone who could experimentally prove an electromagnetic effect in the polarization and depolarization ofinsulators, something predicted by Maxwell's theory.[19][20] Helmholtz was sure Hertz was the most likely candidate to win it.[20] Not seeing any way to build an apparatus to experimentally test this, Hertz thought it was too difficult, and worked onelectromagnetic induction instead. Hertz did produce an analysis of Maxwell's equations during his time at Kiel, showing they did have more validity than the then prevalent "action at a distance" theories.[21]

In the autumn of 1886, after Hertz received his professorship at Karlsruhe, he was experimenting with a pair ofRiess spirals when he noticed that discharging aLeyden jar into one of these coils produced a spark in the other coil. With an idea on how to build an apparatus, Hertz now had a way to proceed with the "Berlin Prize" problem of 1879 on proving Maxwell's theory (although the actual prize had expired uncollected in 1882).[22][23] He used adipole antenna consisting of two collinear one-meter wires with a spark gap between their inner ends, and zinc spheres attached to the outer ends forcapacitance, as a radiator. The antenna was excited by pulses of high voltage of about 30kilovolts applied between the two sides from aRuhmkorff coil. He received the waves with a resonant single-loop antenna with amicrometer spark gap between the ends. This experiment produced and received what are now calledradio waves in thevery high frequency range.

Hertz's first radio transmitter: acapacitance loadeddipole resonator consisting of a pair of one meter copper wires with a 7.5 mm spark gap between them, ending in 30 cm zinc spheres.[17] When aninduction coil applied a high voltage between the two sides, sparks across the spark gap createdstanding waves of radio frequency current in the wires, which radiatedradio waves. Thefrequency of the waves was roughly 50 MHz, about that used in modern television transmitters.

Between 1886 and 1889 Hertz conducted a series of experiments that would prove the effects he was observing were results of Maxwell's predicted electromagnetic waves. Starting in November 1887 with his paper "On Electromagnetic Effects Produced by Electrical Disturbances in Insulators", Hertz sent a series of papers to Helmholtz at the Berlin Academy, including papers in 1888 that showed transversefree spaceelectromagnetic waves traveling at a finite speed over a distance.[23][24] In the apparatus Hertz used, the electric and magnetic fields radiated away from the wires astransverse waves. Hertz had positioned theoscillator about 12 meters from azinc reflecting plate to producestanding waves. Each wave was about 4 meters long.[citation needed] Using the ring detector, he recorded how the wave'smagnitude and component direction varied. Hertz measured Maxwell's waves and demonstrated that thevelocity of these waves was equal to the velocity of light. Theelectric field intensity,polarization andreflection of the waves were also measured by Hertz. These experiments established that light and these waves were both a form of electromagnetic radiation obeying the Maxwell equations.[25]

Hertz's directional spark transmitter(center), ahalf-wave dipole antenna made of two 13 cm brass rods with spark gap at center(closeup left) powered by aRuhmkorff coil, on focal line of a 1.2 m x 2 m cylindrical sheet metalparabolic reflector.[26] It radiated a beam of 66 cm waves with frequency of about 450 MHz. Receiver(right) is similar parabolic dipole antenna withmicrometer spark gap.
Hertz's demonstration ofpolarization of radio waves: the receiver does not respond when antennas are perpendicular as shown, but as receiver is rotated the received signal grows stronger (as shown by length of sparks) until it reaches a maximum when dipoles are parallel.[26]
Another demonstration of polarization: waves pass through polarizing filter to the receiver only when the wires are perpendicular to dipoles(A), not when parallel(B).[26]
Demonstration ofrefraction: radio waves bend when passing through aprism made ofpitch, similarly to light waves when passing through a glass prism.[26]
Hertz's plot ofstanding waves created when radio waves are reflected from a sheet of metal

Hertz did not realize the practical importance of hisradio wave experiments. He stated that,[27][28][29]

It's of no use whatsoever ... this is just an experiment that proves Maestro Maxwell was right—we just have these mysterious electromagnetic waves that we cannot see with the naked eye. But they are there.

Asked about the applications of his discoveries, Hertz replied,[27]

Nothing, I guess

Hertz's proof of the existence of airborne electromagnetic waves led to an explosion of experimentation with this new form of electromagnetic radiation, which was called "Hertzian waves" until around 1910 when the term "radio waves" became current. Within 6 yearsGuglielmo Marconi began developing a radio wave basedwireless telegraphy system,[30] leading to the wide use of radio communication.

Cathode rays

[edit]

In 1883, he tried to prove that the cathode rays are electrically neutral and got what he interpreted as a confident absence of deflection in electrostatic field. However, asJ. J. Thomson explained in 1897, Hertz placed the deflecting electrodes in a highly-conductive area of the tube, resulting in a strong screening effect close to their surface.[31]

Nine years later Hertz began experimenting and demonstrated thatcathode rays could penetrate very thin metal foil (such as aluminium).Philipp Lenard, a student of Heinrich Hertz, further researched this "ray effect". He developed a version of the cathode tube and studied the penetration by X-rays of various materials. However, Lenard did not realize that he was producing X-rays. Hermann von Helmholtz formulated mathematical equations for X-rays. He postulated a dispersion theory beforeRöntgen made his discovery and announcement. It was formed on the basis of the electromagnetic theory of light (Wiedmann's Annalen, Vol. XLVIII). However, he did not work with actual X-rays.[32]

Photoelectric effect

[edit]

Hertz helped establish thephotoelectric effect (which was later explained byAlbert Einstein) when he noticed that acharged object loses its charge more readily when illuminated byultraviolet radiation (UV). In 1887, he made observations of the photoelectric effect and of the production and reception of electromagnetic (EM) waves, published in the journalAnnalen der Physik. His receiver consisted of a coil with aspark gap, whereby a spark would be seen upon detection of EM waves. He placed the apparatus in a darkened box to see the spark better. He observed that the maximum spark length was reduced when in the box. A glass panel placed between the source of EM waves and the receiver absorbed UV that assisted theelectrons in jumping across the gap. When removed, the spark length would increase. He observed no decrease in spark length when he substituted quartz for glass, asquartz does not absorb UV radiation. Hertz concluded his months of investigation and reported the results obtained. He did not further pursue investigation of this effect, nor did he make any attempt at explaining how the observed phenomenon was brought about.[33]

Contact mechanics

[edit]
Main article:Contact mechanics
Memorial of Heinrich Hertz on the campus of theKarlsruhe Institute of Technology, which translates asAt this site, Heinrich Hertz discovered electromagnetic waves in the years 1885–1889

In 1881 and 1882, Hertz published two articles[34][35][36] on what was to become known as the field ofcontact mechanics, which proved to be an important basis for later theories in the field.Joseph Valentin Boussinesq published some critically important observations on Hertz's work, nevertheless establishing this work on contact mechanics to be of immense importance. His work basically summarises how twoaxi-symmetric objects placed in contact will behave underloading, he obtained results based upon the classical theory ofelasticity andcontinuum mechanics. The most significant flaw of his theory was the neglect of any nature ofadhesion between the two solids, which proves to be important as the materials composing the solids start to assume high elasticity. It was natural to neglect adhesion at the time, however, as there were no experimental methods of testing for it.[37]

To develop his theory Hertz used his observation of ellipticalNewton's rings formed upon placing a glass sphere upon a lens as the basis of assuming that the pressure exerted by the sphere follows anelliptical distribution. He used the formation of Newton's rings again while validating his theory with experiments in calculating thedisplacement which the sphere has into the lens.Kenneth L. Johnson, K. Kendall and A. D. Roberts (JKR) used this theory as a basis while calculating the theoretical displacement orindentation depth in the presence of adhesion in 1971.[38] Hertz's theory is recovered from their formulation if the adhesion of the materials is assumed to be zero. Similar to this theory, however using different assumptions,B. V. Derjaguin, V. M. Muller and Y. P. Toporov published another theory in 1975, which came to be known as the DMT theory in the research community, which also recovered Hertz's formulations under the assumption of zero adhesion. This DMT theory proved to be premature and needed several revisions before it came to be accepted as another material contact theory in addition to the JKR theory. Both the DMT and the JKR theories form the basis of contact mechanics upon which all transition contact models are based and used in material parameter prediction innanoindentation andatomic force microscopy. These models are central to the field oftribology and he was named as one of the 23 "Men of Tribology" byDuncan Dowson.[39] Despite preceding his great work on electromagnetism (which he himself considered with his characteristic soberness to be trivial[27]), Hertz's research on contact mechanics has facilitated the age ofnanotechnology.

Hertz also described the "Hertzian cone", a type offracture mode in brittle solids caused by the transmission of stress waves.[40]

Meteorology

[edit]

Hertz always had a deep interest inmeteorology, probably derived from his contacts withWilhelm von Bezold (who was his professor in a laboratory course at the Munich Polytechnic in the summer of 1878). As an assistant to Helmholtz in Berlin, he contributed a few minor articles in the field, including research on theevaporation of liquids,[41] a new kind ofhygrometer, and a graphical means of determining the properties of moist air when subjected toadiabatic changes.[42]

Philosophy of science

[edit]

In the introduction of his 1894 bookPrinciples of Mechanics, Hertz discusses the different "pictures" used to represent physics in his time including the picture ofNewtonian mechanics (based on mass and forces), a second picture (based onconservation of energy andHamilton's principle) and his own picture (based uniquely on space, time, mass and theHertz principle), comparing them in terms of 'permissibility', 'correctness' and 'appropriateness'.[43] Hertz wanted to remove "empty assumptions" and argue against the Newtonian concept offorce and againstaction at a distance.[43] PhilosopherLudwig Wittgenstein inspired by Hertz's work, extended his picture theory into apicture theory of language in his 1921Tractatus Logico-Philosophicus which influencedlogical positivism.[43] Wittgenstein also quotes him in theBlue and Brown Books.[44]

Third Reich treatment

[edit]

Because Hertz's family converted from Judaism to Lutheranism two decades before his birth, his legacy ran afoul of theNazi government in the 1930s, a regime that classified people by "race" instead of religious affiliation.[45][46]

Hertz's name was removed from streets and institutions and there was even a movement to rename the frequency unit named in his honor (hertz) afterHermann von Helmholtz instead, keeping the symbol (Hz) unchanged.[46]

His family was also persecuted for their non-Aryan status. Hertz's youngest daughter, Mathilde, lost a lectureship at Berlin University after the Nazis came to power and within a few years she, her sister, and their mother left Germany and settled in England.[47]

Legacy and honors

[edit]
Heinrich Hertz

Heinrich Hertz's nephew,Gustav Ludwig Hertz was a Nobel Prize winner, and Gustav's sonCarl Helmut Hertz inventedmedical ultrasonography. His daughterMathilde Carmen Hertz was a well-known biologist and comparative psychologist. Hertz's grandnephew Hermann Gerhard Hertz, professor at theUniversity of Karlsruhe, was a pioneer of NMR-spectroscopy and in 1995 published Hertz's laboratory notes.[48]

The SI unithertz (Hz) was established in his honor by theInternational Electrotechnical Commission in 1930 forfrequency, an expression of the number of times that a repeated event occurs per second.[49] It was adopted by theCGPM (Conférence générale des poids et mesures) in 1960, officially replacing the previous name, "cycles per second" (cps).[50]

In 1928 theHeinrich-Hertz Institute for Oscillation Research was founded in Berlin. Today known as theFraunhofer Institute for Telecommunications, Heinrich Hertz Institute, HHI.

In 1969, inEast Germany, a Heinrich Hertz memorial medal[51] was cast.

TheIEEE Heinrich Hertz Medal, established in 1987, is "for outstanding achievements in Hertzian waves[...] presented annually to an individual for achievements which are theoretical or experimental in nature".

TheSubmillimeter Radio Telescope at Mt. Graham, Arizona, constructed in 1992 is named after him.

Acrater that lies on thefar side of theMoon, just behind the eastern limb, is theHertz crater, named in his honor.

On his birthday in 2012, Google honored Hertz with aGoogle doodle, inspired by his life's work, on its home page.[52][53]

Works

[edit]

Books

[edit]
  • Ueber die Induction in rotirenden Kugeln, 1880
    Ueber die Induction in rotirenden Kugeln, 1880
  • Schriften vermischten Inhalts, 1895
    Schriften vermischten Inhalts, 1895

Articles

[edit]
  • Hertz, H.R. "Ueber sehr schnelle electrische Schwingungen",Annalen der Physik, vol. 267, no. 7, p. 421–448, May 1887doi:10.1002/andp.18872670707
  • Hertz, H.R. "Ueber einen Einfluss des ultravioletten Lichtes auf die electrische Entladung",Annalen der Physik, vol. 267, no. 8, p. 983–1000, June 1887doi:10.1002/andp.18872670827
  • Hertz, H.R. "Ueber die Einwirkung einer geradlinigen electrischen Schwingung auf eine benachbarte Strombahn",Annalen der Physik, vol. 270, no. 5, p. 155–170, March 1888doi:10.1002/andp.18882700510
  • Hertz, H.R. "Ueber die Ausbreitungsgeschwindigkeit der electrodynamischen Wirkungen",Annalen der Physik, vol. 270, no. 7, p. 551–569, May 1888doi:10.1002/andp.18882700708
  • Hertz, H. R.(1899)The Principles of Mechanics Presented in a New Form, London, Macmillan, with an introduction byHermann von Helmholtz (English translation ofDie Prinzipien der Mechanik in neuem Zusammenhange dargestellt, Leipzig, posthumously published in 1894).

See also

[edit]

Lists and histories

Electromagnetic radiation

Other

References

[edit]
  1. ^abc"Heinrich Hertz - The Mathematics Genealogy Project".genealogy.math.ndsu.nodak.edu. Retrieved5 June 2025.
  2. ^Stutzman, Warren L.; Thiele, Gary A. (2012).Antenna Theory and Design (3rd ed.). John Wiley & Sons. pp. 391–392.ISBN 978-0470576649.
  3. ^"HERTZ Definition & Meaning".dictionary.com. Retrieved25 May 2025.
  4. ^Krech, Eva-Maria; Stock, Eberhard; Hirschfeld, Ursula; Anders, Lutz Christian (2009).Deutsches Aussprachewörterbuch [German Pronunciation Dictionary] (in German). Berlin: Walter de Gruyter. pp. 575, 580.ISBN 978-3-11-018202-6.
  5. ^Kleiner, Stefan; Knöbl, Ralf (2015) [First published 1962].Das Aussprachewörterbuch [The Pronunciation Dictionary] (in German) (7th ed.). Berlin: Dudenverlag. p. 440.ISBN 978-3-411-04067-4.
  6. ^"Biography: Heinrich Rudolf Hertz". MacTutor History of Mathematics archive. Retrieved2 February 2013.
  7. ^Buchwald 2011, p. 45
  8. ^Buchwald 2011, pp. 51-65
  9. ^Buchwald 2011, p. 218
  10. ^Stathis Psillos, Philosophy of Science A-Z, Edinburgh University Press · 2007, page 107
  11. ^Robertson, O'Connor."Heinrich Rudolf Hertz".MacTutor. University of Saint Andrews, Scotland. Retrieved20 October 2020.
  12. ^Hamburger Friedhöfe » Ohlsdorf » Prominente. Friedhof-hamburg.de. Retrieved 22 August 2014.
  13. ^Plan Ohlsdorfer Friedhof (Map of Ohlsdorf Cemetery). friedhof-hamburg.de.
  14. ^IEEE Institute,Did You Know? Historical ‘Facts’ That Are Not TrueArchived 10 January 2014 at theWayback Machine
  15. ^"Pope Gives Cash To Aid Family of Jew Scientist".Chicago Tribune. 26 March 1938. p. 7. Retrieved18 March 2025 – viaNewspapers.com.
  16. ^Susskind, Charles. (1995).Heinrich Hertz: A Short Life. San Francisco: San Francisco Press.ISBN 0-911302-74-3
  17. ^abAppleyard, Rollo (October 1927)."Pioneers of Electrical Communication part 5 – Heinrich Rudolph Hertz"(PDF).Electrical Communication.6 (2). New York: International Standard Electric Corp.:63–77. Retrieved19 December 2015.The two images shown are p. 66, fig. 3 and p. 70 fig. 9
  18. ^O'Connor, J.J.; Robertson, E.F. (November 1997)."James Clerk Maxwell". School of Mathematical and Computational Sciences University of St Andrews.Archived from the original on 5 November 2021. Retrieved19 June 2021.
  19. ^Heinrich Hertz. nndb.com. Retrieved 22 August 2014.
  20. ^abBaird, Davis, Hughes, R.I.G. and Nordmann, Alfred eds. (1998).Heinrich Hertz: Classical Physicist, Modern Philosopher. New York:Springer-Verlag.ISBN 0-7923-4653-X. p. 49
  21. ^Heilbron, John L. (2005)The Oxford Guide to the History of Physics and Astronomy. Oxford University Press.ISBN 0195171985. p. 148
  22. ^Baird, Davis, Hughes, R.I.G. and Nordmann, Alfred eds. (1998).Heinrich Hertz: Classical Physicist, Modern Philosopher. New York:Springer-Verlag.ISBN 0-7923-4653-X. p. 53
  23. ^abHuurdeman, Anton A. (2003)The Worldwide History of Telecommunications. Wiley.ISBN 0471205052. p. 202
  24. ^"The most important Experiments – The most important Experiments and their Publication between 1886 and 1889". Fraunhofer Heinrich Hertz Institute. Retrieved19 February 2016.
  25. ^Buchwald 2011, pp. 77-91
  26. ^abcdPierce, George Washington (1910).Principles of Wireless Telegraphy. New York: McGraw-Hill Book Co. pp. 51–55.
  27. ^abc"Heinrich Rudolph Hertz".History. Institute of Chemistry, Hebrew Univ. of Jerusalem website. 2004. Archived from the original on 25 September 2009. Retrieved6 March 2018.{{cite web}}: CS1 maint: bot: original URL status unknown (link)
  28. ^Capri, Anton Z. (2007)Quips, quotes, and quanta: an anecdotal history of physics. World Scientific.ISBN 9812709207. p 93.
  29. ^Norton, Andrew (2000).Dynamic Fields and Waves. CRC Press. p. 83.ISBN 0750307196.
  30. ^John S. Belrose, Fessenden and Marconi: Their Differing Technologies and Transatlantic Experiments During the First Decade of this Century, International Conference on 100 Years of Radio -- 5-7 September 1995, ieee.org
  31. ^Thomson, George (1970)."An Unfortunate Experiment: Hertz and the Nature of Cathode Rays".Notes and Records of the Royal Society of London.25 (2):237–242.doi:10.1098/rsnr.1970.0032.ISSN 0035-9149.JSTOR 530878.
  32. ^Buchwald 2011, pp. 151-153
  33. ^Buchwald 2011, p. 244
  34. ^Hertz, Heinrich (1882)."Ueber die Berührung fester elastischer Körper".Journal für die reine und angewandte Mathematik.1882 (92):156–171.doi:10.1515/crll.1882.92.156.S2CID 123604617.
  35. ^Hertz, Heinrich (1882)."Über die Berührung fester elastischer Körper und über die Härte".Verhandlungen des Vereins zur Beförderung des Gewerbefleißes.1882:449–463. Retrieved9 February 2022.
  36. ^Hertz, Heinrich (1986).Miscellaneous Papers. London: Macmillan and Co, Ltd. pp. 146–183. Retrieved13 February 2022.
  37. ^Tevis D. B. Jacobs, C. M. Mate, Kevin T. Turner, Robert W Carpick, Understanding the tip-sample contact: An overview of contact mechanics at the nanoscale, November 2013
  38. ^Johnson, K. L.; Kendall, K.; Roberts, A. D. (1971)."Surface energy and contact of elastic solids"(PDF).Proceedings of the Royal Society A.324 (1558):301–313.Bibcode:1971RSPSA.324..301J.doi:10.1098/rspa.1971.0141.S2CID 137730057.
  39. ^Dowson, Duncan (1 April 1979)."Men of Tribology: Heinrich Rudolph Hertz (1857–1894) and Richard Stribeck (1861–1950)".Journal of Lubrication Technology.101 (2):115–119.doi:10.1115/1.3453287.ISSN 0022-2305.
  40. ^"Purdue University - Study on Hertzian cone crack"
  41. ^Hertz, H. (1882)."Ueber die Verdunstung der Flüssigkeiten, insbesondere des Quecksilbers, im luftleeren Raume".Annalen der Physik.253 (10):177–193.Bibcode:1882AnP...253..177H.doi:10.1002/andp.18822531002.ISSN 1521-3889.
  42. ^Mulligan, J. F.; Hertz, H. G. (1997)."An unpublished lecture by Heinrich Hertz: "On the energy balance of the Earth"".American Journal of Physics.65 (1):36–45.Bibcode:1997AmJPh..65...36M.doi:10.1119/1.18565.
  43. ^abcBarker, Peter (2016),"Hertz, Heinrich Rudolf (1857–94)",Routledge Encyclopedia of Philosophy (1 ed.), London: Routledge,doi:10.4324/9780415249126-q046-1,ISBN 978-0-415-25069-6, retrieved24 August 2023
  44. ^Fielding, James Matthew (2023).The Movement of Thought: Wittgenstein on Time, Change and History. Springer International Publishing. p. 219.
  45. ^Koertge, Noretta. (2007).Dictionary of Scientific Biography. New York:Thomson-Gale.ISBN 0-684-31320-0. Vol. 6, p. 340.
  46. ^abWolff, Stefan L. (2008-01-04)Juden wider Willen – Wie es den Nachkommen des Physikers Heinrich Hertz im NS-Wissenschaftsbetrieb erging. Jüdische Allgemeine.
  47. ^MacRakies K. 1993.Surviving the Swastika: Scientific Research in Nazi Germany. New York, USA: Oxford University Press
  48. ^Hertz, H.G.; Doncel, M.G. (1995). "Heinrich Hertz's Laboratory Notes of 1887".Archive for History of Exact Sciences.49 (3):197–270.doi:10.1007/bf00376092.S2CID 121101068.
  49. ^"IEC History". Iec.ch. Archived fromthe original on 19 May 2013.
  50. ^Brian Taylor, H. Gustav Mueller, Fitting and Dispensing Hearing Aids, Plural Publishing, Incorporated · 2020, page 29
  51. ^Heinrich Rudolf HertzArchived 3 June 2013 at theWayback Machine. Highfields-arc.co.uk. Retrieved 22 August 2014.
  52. ^Albanesius, Chloe (22 February 2012)."Google Doodle Honors Heinrich Hertz, Electromagnetic Wave Pioneer".PC Magazine. Retrieved22 February 2012.
  53. ^Heinrich Rudolf Hertz's 155th Birthday. Google (22 February 2012). Retrieved 22 August 2014.

Further reading

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