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class="vector-toc-numb">2.3</span> <span>Ophthalmic optics</span> </div> </a> <ul id="toc-Ophthalmic_optics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Nerve_physiology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Nerve_physiology"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Nerve physiology</span> </div> </a> <ul id="toc-Nerve_physiology-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Acoustics_and_aesthetics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Acoustics_and_aesthetics"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Acoustics and aesthetics</span> </div> </a> <ul id="toc-Acoustics_and_aesthetics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Electromagnetism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Electromagnetism"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Electromagnetism</span> </div> </a> <ul id="toc-Electromagnetism-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Philosophy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Philosophy"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Philosophy</span> </div> </a> <ul id="toc-Philosophy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Students_and_associates" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Students_and_associates"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Students and associates</span> </div> </a> <ul id="toc-Students_and_associates-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Honours_and_legacy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Honours_and_legacy"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Honours and legacy</span> </div> </a> <ul id="toc-Honours_and_legacy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Works" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Works"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Works</span> </div> </a> <button aria-controls="toc-Works-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Works subsection</span> </button> <ul id="toc-Works-sublist" class="vector-toc-list"> <li id="toc-Translated_works" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Translated_works"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Translated works</span> </div> </a> <ul id="toc-Translated_works-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Citations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Citations"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Citations</span> </div> </a> <ul id="toc-Citations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Hermann von Helmholtz</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 71 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-71" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">71 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Alemannic" lang="gsw" hreflang="gsw" data-title="Hermann von Helmholtz" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%87%D8%B1%D9%85%D8%A7%D9%86_%D9%81%D9%88%D9%86_%D9%87%D9%84%D9%85%D9%87%D9%88%D9%84%D8%AA%D8%B2" title="هرمان فون هلمهولتز – Arabic" lang="ar" hreflang="ar" data-title="هرمان فون هلمهولتز" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Asturian" lang="ast" hreflang="ast" data-title="Hermann von Helmholtz" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%87%D8%B1%D9%85%D8%A7%D9%86_%D9%81%D9%88%D9%86_%D9%87%D9%84%D9%85%D9%87%D9%88%D9%84%D8%AA%D8%B2" title="هرمان فون هلمهولتز – South Azerbaijani" lang="azb" hreflang="azb" data-title="هرمان فون هلمهولتز" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%9B%D1%8E%D0%B4%D0%B2%D1%96%D0%B3_%D0%A4%D0%B5%D1%80%D0%B4%D1%8B%D0%BD%D0%B0%D0%BD%D0%B4_%D0%93%D0%B5%D0%BB%D1%8C%D0%BC%D0%B3%D0%BE%D0%BB%D1%8C%D1%86" title="Герман Людвіг Фердынанд Гельмгольц – Belarusian" lang="be" hreflang="be" data-title="Герман Людвіг Фердынанд Гельмгольц" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A5%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D1%84%D0%BE%D0%BD_%D0%A5%D0%B5%D0%BB%D0%BC%D1%85%D0%BE%D0%BB%D1%86" title="Херман фон Хелмхолц – Bulgarian" lang="bg" hreflang="bg" data-title="Херман фон Хелмхолц" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Bosnian" lang="bs" hreflang="bs" data-title="Hermann von Helmholtz" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Catalan" lang="ca" hreflang="ca" data-title="Hermann von Helmholtz" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%93%D0%B5%D0%BB%D1%8C%D0%BC%D0%B3%D0%BE%D0%BB%D1%8C%D1%86_%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%9B%D1%8E%D0%B4%D0%B2%D0%B8%D0%B3_%D0%A4%D0%B5%D1%80%D0%B4%D0%B8%D0%BD%D0%B0%D0%BD%D0%B4" title="Гельмгольц Герман Людвиг Фердинанд – Chuvash" lang="cv" hreflang="cv" data-title="Гельмгольц Герман Людвиг Фердинанд" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Czech" lang="cs" hreflang="cs" data-title="Hermann von Helmholtz" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Welsh" lang="cy" hreflang="cy" data-title="Hermann von Helmholtz" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Danish" lang="da" hreflang="da" data-title="Hermann von Helmholtz" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – German" lang="de" hreflang="de" data-title="Hermann von Helmholtz" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Estonian" lang="et" hreflang="et" data-title="Hermann von Helmholtz" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A7%CE%AD%CF%81%CE%BC%CE%B1%CE%BD_%CF%86%CE%BF%CE%BD_%CE%A7%CE%AD%CE%BB%CE%BC%CF%87%CE%BF%CE%BB%CF%84%CF%82" title="Χέρμαν φον Χέλμχολτς – Greek" lang="el" hreflang="el" data-title="Χέρμαν φον Χέλμχολτς" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Spanish" lang="es" hreflang="es" data-title="Hermann von Helmholtz" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Esperanto" lang="eo" hreflang="eo" data-title="Hermann von Helmholtz" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Basque" lang="eu" hreflang="eu" data-title="Hermann von Helmholtz" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%87%D8%B1%D9%85%D8%A7%D9%86_%D9%81%D9%88%D9%86_%D9%87%D9%84%D9%85%D9%87%D9%88%D9%84%D8%AA%D8%B2" title="هرمان فون هلمهولتز – Persian" lang="fa" hreflang="fa" data-title="هرمان فون هلمهولتز" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – French" lang="fr" hreflang="fr" data-title="Hermann von Helmholtz" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Irish" lang="ga" hreflang="ga" data-title="Hermann von Helmholtz" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Galician" lang="gl" hreflang="gl" data-title="Hermann von Helmholtz" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%97%A4%EB%A5%B4%EB%A7%8C_%ED%8F%B0_%ED%97%AC%EB%A6%84%ED%99%80%EC%B8%A0" title="헤르만 폰 헬름홀츠 – Korean" lang="ko" hreflang="ko" data-title="헤르만 폰 헬름홀츠" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A5%D6%80%D5%B4%D5%A1%D5%B6_%D5%80%D5%A5%D5%AC%D5%B4%D5%B0%D5%B8%D5%AC%D6%81" title="Հերման Հելմհոլց – Armenian" lang="hy" hreflang="hy" data-title="Հերման Հելմհոլց" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B9%E0%A5%87%E0%A4%B2%E0%A5%8D%E0%A4%AE%E0%A4%B9%E0%A5%8B%E0%A4%B2%E0%A5%8D%E0%A4%9C%E0%A4%BC" title="हेल्महोल्ज़ – Hindi" lang="hi" hreflang="hi" data-title="हेल्महोल्ज़" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Croatian" lang="hr" hreflang="hr" data-title="Hermann von Helmholtz" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Indonesian" lang="id" hreflang="id" data-title="Hermann von Helmholtz" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Icelandic" lang="is" hreflang="is" data-title="Hermann von Helmholtz" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Italian" lang="it" hreflang="it" data-title="Hermann von Helmholtz" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%A8%D7%9E%D7%9F_%D7%A4%D7%95%D7%9F_%D7%94%D7%9C%D7%9E%D7%94%D7%95%D7%9C%D7%A5" title="הרמן פון הלמהולץ – Hebrew" lang="he" hreflang="he" data-title="הרמן פון הלמהולץ" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%B0%E1%83%94%E1%83%A0%E1%83%9B%E1%83%90%E1%83%9C_%E1%83%B0%E1%83%94%E1%83%9A%E1%83%9B%E1%83%B0%E1%83%9D%E1%83%9A%E1%83%AA%E1%83%98" title="ჰერმან ჰელმჰოლცი – Georgian" lang="ka" hreflang="ka" data-title="ჰერმან ჰელმჰოლცი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%93%D0%B5%D0%BB%D1%8C%D0%BC%D0%B3%D0%BE%D0%BB%D1%8C%D1%86" title="Герман Гельмгольц – Kazakh" lang="kk" hreflang="kk" data-title="Герман Гельмгольц" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Cornish" lang="kw" hreflang="kw" data-title="Hermann von Helmholtz" data-language-autonym="Kernowek" data-language-local-name="Cornish" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Haitian Creole" lang="ht" hreflang="ht" data-title="Hermann von Helmholtz" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D1%84%D0%BE%D0%BD_%D0%93%D0%B5%D0%BB%D1%8C%D0%BC%D0%B3%D0%BE%D0%BB%D1%8C%D1%86" title="Герман фон Гельмгольц – Kyrgyz" lang="ky" hreflang="ky" data-title="Герман фон Гельмгольц" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Hermanis_fon_Helmholcs" title="Hermanis fon Helmholcs – Latvian" lang="lv" hreflang="lv" data-title="Hermanis fon Helmholcs" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Hermann_Ludwig_von_Helmholtz" title="Hermann Ludwig von Helmholtz – Hungarian" lang="hu" hreflang="hu" data-title="Hermann Ludwig von Helmholtz" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A5%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D1%84%D0%BE%D0%BD_%D0%A5%D0%B5%D0%BB%D0%BC%D0%BE%D0%BB%D1%86" title="Херман фон Хелмолц – Macedonian" lang="mk" hreflang="mk" data-title="Херман фон Хелмолц" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Hermann_Ludwig_von_Helmholtz" title="Hermann Ludwig von Helmholtz – Malagasy" lang="mg" hreflang="mg" data-title="Hermann Ludwig von Helmholtz" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B9%E0%B5%86%E0%B5%BC%E0%B4%AE%E0%B5%BB_%E0%B4%B5%E0%B5%8B%E0%B5%BA_%E0%B4%B9%E0%B5%86%E0%B5%BD%E0%B4%82%E0%B4%B9%E0%B5%8B%E0%B5%BE%E0%B4%9F%E0%B5%8D%E0%B4%B8%E0%B5%8D" title="ഹെർമൻ വോൺ ഹെൽംഹോൾട്സ് – Malayalam" lang="ml" hreflang="ml" data-title="ഹെർമൻ വോൺ ഹെൽംഹോൾട്സ്" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%B0%E1%83%94%E1%83%A0%E1%83%9B%E1%83%90%E1%83%9C_%E1%83%A4%E1%83%9D%E1%83%9C_%E1%83%B0%E1%83%94%E1%83%9A%E1%83%9B%E1%83%B0%E1%83%9D%E1%83%9A%E1%83%AA%E1%83%98" title="ჰერმან ფონ ჰელმჰოლცი – Mingrelian" lang="xmf" hreflang="xmf" data-title="ჰერმან ფონ ჰელმჰოლცი" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%87%D8%B1%D9%85%D8%A7%D9%86_%D9%81%D9%88%D9%86_%D9%87%D9%84%D9%85%D9%87%D9%88%D9%84%D8%AA%D8%B2" title="هرمان فون هلمهولتز – Egyptian Arabic" lang="arz" hreflang="arz" data-title="هرمان فون هلمهولتز" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Malay" lang="ms" hreflang="ms" data-title="Hermann von Helmholtz" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Dutch" lang="nl" hreflang="nl" data-title="Hermann von Helmholtz" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%98%E3%83%AB%E3%83%9E%E3%83%B3%E3%83%BB%E3%83%95%E3%82%A9%E3%83%B3%E3%83%BB%E3%83%98%E3%83%AB%E3%83%A0%E3%83%9B%E3%83%AB%E3%83%84" title="ヘルマン・フォン・ヘルムホルツ – Japanese" lang="ja" hreflang="ja" data-title="ヘルマン・フォン・ヘルムホルツ" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Hermann von Helmholtz" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Hermann von Helmholtz" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Uzbek" lang="uz" hreflang="uz" data-title="Hermann von Helmholtz" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%DB%81%D8%B1%D9%85%D9%86_%D9%81%D8%A7%D9%86_%DB%81%DB%8C%D9%84%D9%85%DB%81%D9%88%D9%84%D9%B9%D8%B2" title="ہرمن فان ہیلمہولٹز – Western Punjabi" lang="pnb" hreflang="pnb" data-title="ہرمن فان ہیلمہولٹز" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Piedmontese" lang="pms" hreflang="pms" data-title="Hermann von Helmholtz" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Polish" lang="pl" hreflang="pl" data-title="Hermann von Helmholtz" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Portuguese" lang="pt" hreflang="pt" data-title="Hermann von Helmholtz" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Romanian" lang="ro" hreflang="ro" data-title="Hermann von Helmholtz" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%93%D0%B5%D0%BB%D1%8C%D0%BC%D0%B3%D0%BE%D0%BB%D1%8C%D1%86,_%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%9B%D1%8E%D0%B4%D0%B2%D0%B8%D0%B3_%D0%A4%D0%B5%D1%80%D0%B4%D0%B8%D0%BD%D0%B0%D0%BD%D0%B4" title="Гельмгольц, Герман Людвиг Фердинанд – Russian" lang="ru" hreflang="ru" data-title="Гельмгольц, Герман Людвиг Фердинанд" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Scots" lang="sco" hreflang="sco" data-title="Hermann von Helmholtz" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Simple English" lang="en-simple" hreflang="en-simple" data-title="Hermann von Helmholtz" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Slovak" lang="sk" hreflang="sk" data-title="Hermann von Helmholtz" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Hermann_Ludwig_Ferdinand_von_Helmholtz" title="Hermann Ludwig Ferdinand von Helmholtz – Slovenian" lang="sl" hreflang="sl" data-title="Hermann Ludwig Ferdinand von Helmholtz" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A5%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D1%84%D0%BE%D0%BD_%D0%A5%D0%B5%D0%BB%D0%BC%D1%85%D0%BE%D0%BB%D1%86" title="Херман фон Хелмхолц – Serbian" lang="sr" hreflang="sr" data-title="Херман фон Хелмхолц" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Hermann von Helmholtz" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Sundanese" lang="su" hreflang="su" data-title="Hermann von Helmholtz" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Finnish" lang="fi" hreflang="fi" data-title="Hermann von Helmholtz" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Swedish" lang="sv" hreflang="sv" data-title="Hermann von Helmholtz" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%81%E0%B8%AE%E0%B8%A3%E0%B9%8C%E0%B8%A1%E0%B8%B1%E0%B8%99_%E0%B8%9F%E0%B9%87%E0%B8%AD%E0%B8%99_%E0%B9%80%E0%B8%AE%E0%B9%87%E0%B8%A5%E0%B9%8C%E0%B8%A1%E0%B8%AE%E0%B9%87%E0%B8%AD%E0%B8%A5%E0%B8%97%E0%B8%8B%E0%B9%8C" title="แฮร์มัน ฟ็อน เฮ็ล์มฮ็อลทซ์ – Thai" lang="th" hreflang="th" data-title="แฮร์มัน ฟ็อน เฮ็ล์มฮ็อลทซ์" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Turkish" lang="tr" hreflang="tr" data-title="Hermann von Helmholtz" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D1%84%D0%BE%D0%BD_%D0%93%D0%B5%D0%BB%D1%8C%D0%BC%D0%B3%D0%BE%D0%BB%D1%8C%D1%86" title="Герман фон Гельмгольц – Ukrainian" lang="uk" hreflang="uk" data-title="Герман фон Гельмгольц" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Vietnamese" lang="vi" hreflang="vi" data-title="Hermann von Helmholtz" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz – Waray" lang="war" hreflang="war" data-title="Hermann von Helmholtz" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%B5%AB%E5%B0%94%E6%9B%BC%C2%B7%E5%86%AF%C2%B7%E4%BA%A5%E5%A7%86%E9%9C%8D%E5%85%B9" title="赫尔曼·冯·亥姆霍兹 – Wu" lang="wuu" hreflang="wuu" data-title="赫尔曼·冯·亥姆霍兹" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%BA%A5%E5%A7%86%E9%9C%8D%E8%8C%B2" title="亥姆霍茲 – Cantonese" lang="yue" hreflang="yue" data-title="亥姆霍茲" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%B5%AB%E5%B0%94%E6%9B%BC%C2%B7%E5%86%AF%C2%B7%E4%BA%A5%E5%A7%86%E9%9C%8D%E5%85%B9" title="赫尔曼·冯·亥姆霍兹 – Chinese" lang="zh" hreflang="zh" data-title="赫尔曼·冯·亥姆霍兹" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q60024#sitelinks-wikipedia" title="Edit interlanguage links" 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<div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">German physicist and physiologist (1821–1894)</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Helmholtz" redirects here. For other uses, see <a href="/wiki/Helmholtz_(disambiguation)" class="mw-disambig" title="Helmholtz (disambiguation)">Helmholtz (disambiguation)</a>.</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Hermann von Helmholtz</div><div class="honorific-suffix" style="font-size: 77%; font-weight: normal;"><span class="nobold noexcerpt nowraplinks" style="font-size:;"><span style="font-size: 100%;"><a href="/wiki/Foreign_Member_of_the_Royal_Society" class="mw-redirect" title="Foreign Member of the Royal Society">ForMemRS</a></span></span></div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Hermann_von_Helmholtz.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Hermann_von_Helmholtz.jpg/220px-Hermann_von_Helmholtz.jpg" decoding="async" width="220" height="286" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c7/Hermann_von_Helmholtz.jpg/330px-Hermann_von_Helmholtz.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/c/c7/Hermann_von_Helmholtz.jpg 2x" data-file-width="338" data-file-height="440" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><div style="display:inline" class="nickname">Hermann Ludwig Ferdinand Helmholtz</div><br /><span style="display:none">(<span class="bday">1821-08-31</span>)</span>31 August 1821<br /><div style="display:inline" class="birthplace"><a href="/wiki/Potsdam" title="Potsdam">Potsdam</a>, <a href="/wiki/Province_of_Brandenburg" title="Province of Brandenburg">Province of Brandenburg</a>, <a href="/wiki/Kingdom_of_Prussia" title="Kingdom of Prussia">Kingdom of Prussia</a>, <a href="/wiki/German_Confederation" title="German Confederation">German Confederation</a></div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">8 September 1894<span style="display:none">(1894-09-08)</span> (aged 73)<br /><div style="display:inline" class="deathplace"><a href="/wiki/Charlottenburg" title="Charlottenburg">Charlottenburg</a>, Kingdom of Prussia, <a href="/wiki/German_Empire" title="German Empire">German Empire</a></div></td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/w/index.php?title=Medizinisch-chirurgisches_Friedrich-Wilhelm-Institut&action=edit&redlink=1" class="new" title="Medizinisch-chirurgisches Friedrich-Wilhelm-Institut (page does not exist)">Medizinisch-chirurgisches Friedrich-Wilhelm-Institut</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://de.wikipedia.org/wiki/Medizinisch-chirurgisches_Friedrich-Wilhelm-Institut" class="extiw" title="de:Medizinisch-chirurgisches Friedrich-Wilhelm-Institut">de</a>]</span> (<a href="/wiki/Doctor_of_Medicine" title="Doctor of Medicine">MD</a>)</td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><div class="collapsible-list mw-collapsible mw-collapsed" style="text-align: left;"> <div style="line-height: 1.6em; font-weight: bold;"><div><style data-mw-deduplicate="TemplateStyles:r886047488">.mw-parser-output .nobold{font-weight:normal}</style><span class="nobold"><i>See list</i></span></div></div> <ul class="mw-collapsible-content" style="margin-top: 0; margin-bottom: 0; line-height: inherit; list-style: none; margin-left: 0;"><li style="line-height: inherit; margin: 0">Studies in the <a href="/wiki/Conservation_of_energy" title="Conservation of energy">conservation of energy</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Helmholtz_theorem_(classical_mechanics)" title="Helmholtz theorem (classical mechanics)">Helmholtz classical theorem</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Helmholtz_coil" title="Helmholtz coil">Helmholtz coil</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Helmholtz_condition" class="mw-redirect" title="Helmholtz condition">Helmholtz condition</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Helmholtz_decomposition" title="Helmholtz decomposition">Helmholtz decomposition</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Helmholtz_equation" title="Helmholtz equation">Helmholtz equation</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Helmholtz_free_energy" title="Helmholtz free energy">Helmholtz free energy</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Free_entropy#Massieu_potential_/_Helmholtz_free_entropy" title="Free entropy">Helmholtz free entropy</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Helmholtz_layer" class="mw-redirect" title="Helmholtz layer">Helmholtz layer</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Helmholtz_minimum_dissipation_theorem" title="Helmholtz minimum dissipation theorem">Helmholtz minimum dissipation theorem</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Violin_acoustics#Helmholtz_motion" title="Violin acoustics">Helmholtz motion</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Helmholtz_pitch_notation" title="Helmholtz pitch notation">Helmholtz pitch notation</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Helmholtz_reciprocity" title="Helmholtz reciprocity">Helmholtz reciprocity</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Helmholtz_resonance" title="Helmholtz resonance">Helmholtz resonance</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Helmholtz_temperament" class="mw-redirect" title="Helmholtz temperament">Helmholtz temperament</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Helmholtz%27s_theorems" title="Helmholtz's theorems">Helmholtz's theorems</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Helmholtz%E2%80%93Kohlrausch_effect" title="Helmholtz–Kohlrausch effect">Helmholtz–Kohlrausch effect</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Helmholtz-Smoluchowski_equation" class="mw-redirect" title="Helmholtz-Smoluchowski equation">Helmholtz–Smoluchowski equation</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Helmholtz-Ellis_notation" class="mw-redirect" title="Helmholtz-Ellis notation">Helmholtz–Ellis notation</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Helmholtz%E2%80%93Th%C3%A9venin_theorem" class="mw-redirect" title="Helmholtz–Thévenin theorem">Helmholtz–Thévenin theorem</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Gibbs%E2%80%93Helmholtz_equation" title="Gibbs–Helmholtz equation">Gibbs–Helmholtz equation</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Kelvin%E2%80%93Helmholtz_instability" title="Kelvin–Helmholtz instability">Kelvin–Helmholtz instability</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Smith%E2%80%93Helmholtz_invariant" title="Smith–Helmholtz invariant">Smith–Helmholtz invariant</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Kelvin%E2%80%93Helmholtz_mechanism" title="Kelvin–Helmholtz mechanism">Kelvin–Helmholtz mechanism</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Young%E2%80%93Helmholtz_theory" title="Young–Helmholtz theory">Young–Helmholtz theory</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Additive_synthesis" title="Additive synthesis">Additive synthesis</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Efference_copy" title="Efference copy">Efference copy</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Entoptic_phenomenon" title="Entoptic phenomenon">Entoptic phenomenon</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Heat_death_paradox" title="Heat death paradox">Heat death paradox</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Hydrodynamic_stability" title="Hydrodynamic stability">Hydrodynamic stability</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Keratometer" title="Keratometer">Keratometer</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Ophthalmoscopy" title="Ophthalmoscopy">Ophthalmoscopy</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Place_theory_(hearing)" class="mw-redirect" title="Place theory (hearing)">Place theory</a></li><li style="line-height: inherit; margin: 0"> <a href="/wiki/Prism_adaptation" title="Prism adaptation">Prism adaptation</a></li><li style="line-height: inherit; margin: 0"><a href="/wiki/Pure_tone" title="Pure tone">Pure tone</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Unconscious_inference" title="Unconscious inference">Unconscious inference</a> </li><li style="line-height: inherit; margin: 0"><a href="/wiki/Vortex_ring" title="Vortex ring">Vortex ring</a> </li></ul> </div></td></tr><tr><th scope="row" class="infobox-label">Spouse</th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1151524712">.mw-parser-output .marriage-line-margin2px{line-height:0;margin-bottom:-2px}.mw-parser-output .marriage-line-margin3px{line-height:0;margin-bottom:-3px}.mw-parser-output .marriage-display-ws{display:inline;white-space:nowrap}</style> <div class="marriage-display-ws"><div style="display:inline-block;line-height:normal;"><a href="/wiki/Anna_von_Mohl" class="mw-redirect" title="Anna von Mohl">Anna von Mohl</a></div> <div style="display:inline-block;"></div>(<abbr title="married">m.</abbr> 1861)<wbr /></div></td></tr><tr><th scope="row" class="infobox-label">Children</th><td class="infobox-data">3</td></tr><tr><th scope="row" class="infobox-label">Relatives</th><td class="infobox-data"><a href="/wiki/Anna_Augusta_Von_Helmholtz-Phelan" title="Anna Augusta Von Helmholtz-Phelan">Anna Augusta Von Helmholtz-Phelan</a> (grand-niece)</td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"><ul><li><a href="/wiki/Fellow_of_the_Royal_Society#Foreign_member" title="Fellow of the Royal Society">ForMemRS</a> (1860)</li><li><a href="/wiki/Croonian_Medal" title="Croonian Medal">Croonian Medal</a> (1864)</li><li><a href="/wiki/Matteucci_Medal" title="Matteucci Medal">Matteucci Medal</a> (1868)</li><li><a href="/wiki/Copley_Medal" title="Copley Medal">Copley Medal</a> (1873)</li><li><a href="/wiki/Pour_le_M%C3%A9rite#Civil_class" title="Pour le Mérite"><i>Pour le Mérite</i></a> (1873)</li><li><a href="/wiki/Faraday_Lectureship_Prize" title="Faraday Lectureship Prize">Faraday Lectureship Prize</a> (1881)</li><li><a href="/wiki/Albert_Medal_(Royal_Society_of_Arts)" title="Albert Medal (Royal Society of Arts)">Albert Medal</a> (1888)</li></ul></div></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Physics" title="Physics">Physics</a><br /><a href="/wiki/Physiology" title="Physiology">Physiology</a></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"> <ul><li><a href="/wiki/University_of_K%C3%B6nigsberg" title="University of Königsberg">University of Königsberg</a> (1849–1855)</li> <li><a href="/wiki/University_of_Bonn" title="University of Bonn">University of Bonn</a> (1855–1858)</li> <li><a href="/wiki/University_of_Heidelberg" class="mw-redirect" title="University of Heidelberg">University of Heidelberg</a> (1858–1871)</li> <li><span class="nowrap"><a href="/wiki/University_of_Berlin" class="mw-redirect" title="University of Berlin">University of Berlin</a> (1871–1888)</span></li></ul> </div></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Thesis" title="Thesis">Thesis</a></th><td class="infobox-data"><i><a rel="nofollow" class="external text" href="http://archiv.ub.uni-heidelberg.de/volltextserver/13299/">De fabrica systematis nervosi evertebratorum</a></i> <span style="font-size:97%;">(1842)</span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Doctoral_advisor" title="Doctoral advisor">Doctoral advisor</a></th><td class="infobox-data"><a href="/wiki/Johannes_Peter_M%C3%BCller" title="Johannes Peter Müller">Johannes Peter Müller</a></td></tr><tr><th scope="row" class="infobox-label">Doctoral students</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li><a href="/wiki/Lor%C3%A1nd_E%C3%B6tv%C3%B6s" title="Loránd Eötvös">Loránd Eötvös</a></li><li><a href="/wiki/Heinrich_Hertz" title="Heinrich Hertz">Heinrich Hertz</a></li><li><a href="/wiki/Gabriel_Lippmann" title="Gabriel Lippmann">Gabriel Lippmann</a></li><li><a href="/wiki/Otto_Lummer" title="Otto Lummer">Otto Lummer</a></li><li><a href="/wiki/Albert_A._Michelson" title="Albert A. Michelson">Albert A. Michelson</a></li><li><a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a></li><li><a href="/wiki/Mihajlo_Pupin" title="Mihajlo Pupin">Mihajlo Pupin</a></li><li><a href="/wiki/Friedrich_Schottky" title="Friedrich Schottky">Friedrich Schottky</a></li><li><a href="/wiki/Arthur_Gordon_Webster" title="Arthur Gordon Webster">Arthur Gordon Webster</a></li><li><a href="/wiki/Max_Wien" title="Max Wien">Max Wien</a></li><li><a href="/wiki/Wilhelm_Wien" title="Wilhelm Wien">Wilhelm Wien</a></li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Other notable students</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"><ul><li><a href="/wiki/%C3%89mile_Boutroux" title="Émile Boutroux">Émile Boutroux</a></li><li><a href="/wiki/Johannes_von_Kries" title="Johannes von Kries">Johannes von Kries</a><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></li><li><a href="/wiki/Edward_Leamington_Nichols" title="Edward Leamington Nichols">Edward Nichols</a></li><li><a href="/wiki/Henry_Augustus_Rowland" title="Henry Augustus Rowland">Henry Augustus Rowland</a></li><li><a href="/wiki/Wilhelm_Wundt" title="Wilhelm Wundt">Wilhelm Wundt</a></li></ul></div></td></tr><tr style="display:none"><td colspan="2"> </td></tr><tr><th colspan="2" class="infobox-header">Signature</th></tr><tr><td colspan="2" class="infobox-full-data"><span class="infobox-signature skin-invert" typeof="mw:File"><a href="/wiki/File:Hermann.von.Helmholtz.Signature.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Hermann.von.Helmholtz.Signature.png/150px-Hermann.von.Helmholtz.Signature.png" decoding="async" width="150" height="103" class="mw-file-element" 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class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><th class="sidebar-title" style="padding-bottom:0.3em;border-bottom:1px solid #aaa;"><a href="/wiki/Thermodynamics" title="Thermodynamics">Thermodynamics</a></th></tr><tr><td class="sidebar-image" style="display:block;margin:0.3em 0 0.4em;"><span class="mw-default-size skin-invert-image" typeof="mw:File/Frameless"><a href="/wiki/Carnot_heat_engine" title="Carnot heat engine"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Carnot_heat_engine_2.svg/220px-Carnot_heat_engine_2.svg.png" decoding="async" width="220" height="97" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Carnot_heat_engine_2.svg/330px-Carnot_heat_engine_2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Carnot_heat_engine_2.svg/440px-Carnot_heat_engine_2.svg.png 2x" data-file-width="840" data-file-height="370" /></a></span><div class="sidebar-caption">The classical <a href="/wiki/Carnot_heat_engine" title="Carnot heat engine">Carnot heat engine</a></div></td></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c">Branches</div></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Thermodynamics" title="Thermodynamics">Classical</a></li> <li><a href="/wiki/Statistical_mechanics" title="Statistical mechanics">Statistical</a></li> <li><a href="/wiki/Chemical_thermodynamics" title="Chemical thermodynamics">Chemical</a></li> <li><a href="/wiki/Quantum_thermodynamics" title="Quantum thermodynamics">Quantum thermodynamics</a></li></ul> </div> <ul><li><a href="/wiki/Equilibrium_thermodynamics" title="Equilibrium thermodynamics">Equilibrium</a> / <a href="/wiki/Non-equilibrium_thermodynamics" title="Non-equilibrium thermodynamics">Non-equilibrium</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Laws_of_thermodynamics" title="Laws of thermodynamics">Laws</a></div></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Zeroth_law_of_thermodynamics" title="Zeroth law of thermodynamics">Zeroth</a></li> <li><a href="/wiki/First_law_of_thermodynamics" title="First law of thermodynamics">First</a></li> <li><a href="/wiki/Second_law_of_thermodynamics" title="Second law of thermodynamics">Second</a></li> <li><a href="/wiki/Third_law_of_thermodynamics" title="Third law of thermodynamics">Third</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Thermodynamic_system" title="Thermodynamic system">Systems</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Closed_system" title="Closed system">Closed system</a></li> <li><a href="/wiki/Thermodynamic_system#Open_system" title="Thermodynamic system">Open system</a></li> <li><a href="/wiki/Isolated_system" title="Isolated system">Isolated system</a></li></ul> <table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base, #202122 ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Thermodynamic_state" title="Thermodynamic state">State</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Equation_of_state" title="Equation of state">Equation of state</a></li> <li><a href="/wiki/Ideal_gas" title="Ideal gas">Ideal gas</a></li> <li><a href="/wiki/Real_gas" title="Real gas">Real gas</a></li> <li><a href="/wiki/State_of_matter" title="State of matter">State of matter</a></li> <li><a href="/wiki/Phase_(matter)" title="Phase (matter)">Phase (matter)</a></li> <li><a href="/wiki/Thermodynamic_equilibrium" title="Thermodynamic equilibrium">Equilibrium</a></li> <li><a href="/wiki/Control_volume" title="Control volume">Control volume</a></li> <li><a href="/wiki/Thermodynamic_instruments" title="Thermodynamic instruments">Instruments</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Thermodynamic_process" title="Thermodynamic process">Processes</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Isobaric_process" title="Isobaric process">Isobaric</a></li> <li><a href="/wiki/Isochoric_process" title="Isochoric process">Isochoric</a></li> <li><a href="/wiki/Isothermal_process" title="Isothermal process">Isothermal</a></li> <li><a href="/wiki/Adiabatic_process" title="Adiabatic process">Adiabatic</a></li> <li><a href="/wiki/Isentropic_process" title="Isentropic process">Isentropic</a></li> <li><a href="/wiki/Isenthalpic_process" title="Isenthalpic process">Isenthalpic</a></li> <li><a href="/wiki/Quasistatic_process" title="Quasistatic process">Quasistatic</a></li> <li><a href="/wiki/Polytropic_process" title="Polytropic process">Polytropic</a></li> <li><a href="/wiki/Free_expansion" class="mw-redirect" title="Free expansion">Free expansion</a></li> <li><a href="/wiki/Reversible_process_(thermodynamics)" title="Reversible process (thermodynamics)">Reversibility</a></li> <li><a href="/wiki/Irreversible_process" title="Irreversible process">Irreversibility</a></li> <li><a href="/wiki/Endoreversible_thermodynamics" title="Endoreversible thermodynamics">Endoreversibility</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Thermodynamic_cycle" title="Thermodynamic cycle">Cycles</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Heat_engine" title="Heat engine">Heat engines</a></li> <li><a href="/wiki/Heat_pump_and_refrigeration_cycle" title="Heat pump and refrigeration cycle">Heat pumps</a></li> <li><a href="/wiki/Thermal_efficiency" title="Thermal efficiency">Thermal efficiency</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/List_of_thermodynamic_properties" title="List of thermodynamic properties">System properties</a></div></div><div class="sidebar-list-content mw-collapsible-content"><div style="font-size:90%;padding-bottom:0.2em;border-bottom:1px solid #aaa;">Note: <a href="/wiki/Conjugate_variables_(thermodynamics)" title="Conjugate variables (thermodynamics)">Conjugate variables</a> in <i>italics</i></div> <table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base, #202122 ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none;margin-top:0.4em;"><tbody><tr><td class="sidebar-content" style="padding-bottom:0.7em;"> <ul><li><a href="/wiki/Thermodynamic_diagrams" title="Thermodynamic diagrams">Property diagrams</a></li> <li><a href="/wiki/Intensive_and_extensive_properties" title="Intensive and extensive properties">Intensive and extensive properties</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Process_function" title="Process function">Process functions</a></th></tr><tr><td class="sidebar-content" style="padding-bottom:0.7em;;padding-bottom:0.4em;"> <div class="hlist"> <ul><li><a href="/wiki/Work_(thermodynamics)" title="Work (thermodynamics)">Work</a></li> <li><a href="/wiki/Heat" title="Heat">Heat</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/State_function" title="State function">Functions of state</a></th></tr><tr><td class="sidebar-content" style="padding-bottom:0.7em;"> <ul><li><a href="/wiki/Thermodynamic_temperature" title="Thermodynamic temperature">Temperature</a> / <i><a href="/wiki/Entropy" title="Entropy">Entropy</a></i> (<a href="/wiki/Introduction_to_entropy" title="Introduction to entropy">introduction</a>)</li> <li><a href="/wiki/Pressure" title="Pressure">Pressure</a> / <i><a href="/wiki/Volume_(thermodynamics)" title="Volume (thermodynamics)">Volume</a></i></li> <li><a href="/wiki/Chemical_potential" title="Chemical potential">Chemical potential</a> / <i><a href="/wiki/Particle_number" title="Particle number">Particle number</a></i></li> <li><a href="/wiki/Vapor_quality" title="Vapor quality">Vapor quality</a></li> <li><a href="/wiki/Reduced_properties" title="Reduced properties">Reduced properties</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Material_properties_(thermodynamics)" title="Material properties (thermodynamics)">Material properties</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Thermodynamic_databases_for_pure_substances" title="Thermodynamic databases for pure substances">Property databases</a></li></ul> <div style="font-size:90%;margin-top:0.4em;border-top:1px solid #aaa;"> <table> <tbody><tr><td style="vertical-align:middle; text-align:right"><a href="/wiki/Heat_capacity" title="Heat capacity">Specific heat capacity</a> </td> <td style="vertical-align:middle; text-align:left"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/891d40a9b18752b04065caee655d008b3ec11428" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.46ex; height:1.676ex;" alt="{\displaystyle c=}"></span></td> <td><table><tbody><tr><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span></td><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c609f4d3c5692ea4495479ef47594dc67f9fa464" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.817ex; height:2.176ex;" alt="{\displaystyle \partial S}"></span></td></tr><tr><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span></td><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/504aa558fff3d00d10b03cadb1085cb0b7bdc631" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.954ex; height:2.176ex;" alt="{\displaystyle \partial T}"></span></td></tr></tbody></table></td></tr> <tr><td style="vertical-align:middle; text-align:right"><a href="/wiki/Compressibility" title="Compressibility">Compressibility</a> </td> <td style="vertical-align:middle; text-align:left"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta =-}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <mo>−</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta =-}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b01c042bf1456bd4d2a8caed1f4912820a7ecbb3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.239ex; height:2.509ex;" alt="{\displaystyle \beta =-}"></span></td> <td><table><tbody><tr><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}"></span></td><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cecdd9d069fa84159940068fc11a91b6b3b9ee4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.105ex; height:2.176ex;" alt="{\displaystyle \partial V}"></span></td></tr><tr><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span></td><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebc4a48eb2412f08b54fe438b5139c88f9cfa372" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.487ex; height:2.509ex;" alt="{\displaystyle \partial p}"></span></td></tr></tbody></table></td></tr> <tr><td style="vertical-align:middle; text-align:right"><a href="/wiki/Thermal_expansion" title="Thermal expansion">Thermal expansion</a> </td> <td style="vertical-align:middle; text-align:left"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha =}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha =}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a92d4583d351f08c1c70985f0c843b2fff1b01e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.941ex; height:1.676ex;" alt="{\displaystyle \alpha =}"></span></td> <td><table><tbody><tr><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}"></span></td><td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cecdd9d069fa84159940068fc11a91b6b3b9ee4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.105ex; height:2.176ex;" alt="{\displaystyle \partial V}"></span></td></tr><tr><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span></td><td style="border-top:solid 1px black;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \partial T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∂</mi> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \partial T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/504aa558fff3d00d10b03cadb1085cb0b7bdc631" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.954ex; height:2.176ex;" alt="{\displaystyle \partial T}"></span></td></tr></tbody></table></td></tr> </tbody></table></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Thermodynamic_equations" title="Thermodynamic equations">Equations</a></div></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Carnot%27s_theorem_(thermodynamics)" title="Carnot's theorem (thermodynamics)">Carnot's theorem</a></li> <li><a href="/wiki/Clausius_theorem" title="Clausius theorem">Clausius theorem</a></li> <li><a href="/wiki/Fundamental_thermodynamic_relation" title="Fundamental thermodynamic relation">Fundamental relation</a></li> <li><a href="/wiki/Ideal_gas_law" title="Ideal gas law">Ideal gas law</a></li></ul> </div> <ul><li><a href="/wiki/Maxwell_relations" title="Maxwell relations">Maxwell relations</a></li> <li><a href="/wiki/Onsager_reciprocal_relations" title="Onsager reciprocal relations">Onsager reciprocal relations</a></li> <li><a href="/wiki/Bridgman%27s_thermodynamic_equations" title="Bridgman's thermodynamic equations">Bridgman's equations</a></li> <li><i><a href="/wiki/Table_of_thermodynamic_equations" title="Table of thermodynamic equations">Table of thermodynamic equations</a></i></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Thermodynamic_potential" title="Thermodynamic potential">Potentials</a></div></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Thermodynamic_free_energy" title="Thermodynamic free energy">Free energy</a></li> <li><a href="/wiki/Free_entropy" title="Free entropy">Free entropy</a></li></ul> </div> <div class="plainlist"><ul><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Internal_energy" title="Internal energy">Internal energy</a><br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U(S,V)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo>,</mo> <mi>V</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U(S,V)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/921f33f9c6551562ec836007b035c2de6323d2d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.912ex; height:2.843ex;" alt="{\displaystyle U(S,V)}"></span></li><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Enthalpy" title="Enthalpy">Enthalpy</a><br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H(S,p)=U+pV}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> <mo stretchy="false">(</mo> <mi>S</mi> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>U</mi> <mo>+</mo> <mi>p</mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H(S,p)=U+pV}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6407d78e5f39d07f70e2414a92e08e2e068519f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.254ex; height:2.843ex;" alt="{\displaystyle H(S,p)=U+pV}"></span></li><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Helmholtz_free_energy" title="Helmholtz free energy">Helmholtz free energy</a><br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A(T,V)=U-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>V</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>U</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A(T,V)=U-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e93692f031ba6484d82731c54db83a69daed3f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.867ex; height:2.843ex;" alt="{\displaystyle A(T,V)=U-TS}"></span></li><li style="font-size:110%;line-height:1.6em;padding-bottom:0.5em;"><a href="/wiki/Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a><br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G(T,p)=H-TS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>H</mi> <mo>−</mo> <mi>T</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G(T,p)=H-TS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8dd7a8f0b8ae04963da133e3b202432e1b6caed4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.614ex; height:2.843ex;" alt="{\displaystyle G(T,p)=H-TS}"></span></li></ul></div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c"><div class="hlist"><ul><li>History</li><li>Culture</li></ul></div></div></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base, #202122 ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> History</th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/History_of_thermodynamics" title="History of thermodynamics">General</a></li> <li><a href="/wiki/History_of_entropy" title="History of entropy">Entropy</a></li> <li><a href="/wiki/Gas_laws" title="Gas laws">Gas laws</a></li></ul> </div> <ul><li><a href="/wiki/History_of_perpetual_motion_machines" title="History of perpetual motion machines">"Perpetual motion" machines</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/Philosophy_of_thermal_and_statistical_physics" class="mw-redirect" title="Philosophy of thermal and statistical physics">Philosophy</a></th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Entropy_(arrow_of_time)" class="mw-redirect" title="Entropy (arrow of time)">Entropy and time</a></li> <li><a href="/wiki/Entropy_and_life" title="Entropy and life">Entropy and life</a></li> <li><a href="/wiki/Brownian_ratchet" title="Brownian ratchet">Brownian ratchet</a></li> <li><a href="/wiki/Maxwell%27s_demon" title="Maxwell's demon">Maxwell's demon</a></li> <li><a href="/wiki/Heat_death_paradox" title="Heat death paradox">Heat death paradox</a></li> <li><a href="/wiki/Loschmidt%27s_paradox" title="Loschmidt's paradox">Loschmidt's paradox</a></li> <li><a href="/wiki/Synergetics_(Haken)" title="Synergetics (Haken)">Synergetics</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> Theories</th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Caloric_theory" title="Caloric theory">Caloric theory</a></li></ul> </div> <ul><li><a href="/wiki/Vis_viva" title="Vis viva"><i>Vis viva</i> <span style="font-size:85%;">("living force")</span></a></li> <li><a href="/wiki/Mechanical_equivalent_of_heat" title="Mechanical equivalent of heat">Mechanical equivalent of heat</a></li> <li><a href="/wiki/Power_(physics)" title="Power (physics)">Motive power</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <a href="/wiki/List_of_important_publications_in_physics" title="List of important publications in physics">Key publications</a></th></tr><tr><td class="sidebar-content"> <ul><li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><i><a href="/wiki/An_Inquiry_Concerning_the_Source_of_the_Heat_Which_Is_Excited_by_Friction" title="An Inquiry Concerning the Source of the Heat Which Is Excited by Friction">An Inquiry Concerning the<br />Source ... Friction</a></i></div></li> <li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><i><a href="/wiki/On_the_Equilibrium_of_Heterogeneous_Substances" title="On the Equilibrium of Heterogeneous Substances">On the Equilibrium of<br />Heterogeneous Substances</a></i></div></li> <li><div style="display:inline-block; padding:0.2em 0.4em; line-height:1.2em;"><i><a href="/wiki/Reflections_on_the_Motive_Power_of_Fire" title="Reflections on the Motive Power of Fire">Reflections on the<br />Motive Power of Fire</a></i></div></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> Timelines</th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Timeline_of_thermodynamics" title="Timeline of thermodynamics">Thermodynamics</a></li> <li><a href="/wiki/Timeline_of_heat_engine_technology" title="Timeline of heat engine technology">Heat engines</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="background:#eaeaff;font-style:italic;"> <div class="hlist"><ul><li>Art</li><li>Education</li></ul></div></th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Maxwell%27s_thermodynamic_surface" title="Maxwell's thermodynamic surface">Maxwell's thermodynamic surface</a></li> <li><a href="/wiki/Entropy_(energy_dispersal)" title="Entropy (energy dispersal)">Entropy as energy dispersal</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c">Scientists</div></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Bernoulli</a></li> <li><a href="/wiki/Ludwig_Boltzmann" title="Ludwig Boltzmann">Boltzmann</a></li> <li><a href="/wiki/Percy_Williams_Bridgman" title="Percy Williams Bridgman">Bridgman</a></li> <li><a href="/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory">Carathéodory</a></li> <li><a href="/wiki/Nicolas_L%C3%A9onard_Sadi_Carnot" title="Nicolas Léonard Sadi Carnot">Carnot</a></li> <li><a href="/wiki/Beno%C3%AEt_Paul_%C3%89mile_Clapeyron" class="mw-redirect" title="Benoît Paul Émile Clapeyron">Clapeyron</a></li> <li><a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Clausius</a></li> <li><a href="/wiki/Th%C3%A9ophile_de_Donder" title="Théophile de Donder">de Donder</a></li> <li><a href="/wiki/Pierre_Duhem" title="Pierre Duhem">Duhem</a></li> <li><a href="/wiki/Josiah_Willard_Gibbs" title="Josiah Willard Gibbs">Gibbs</a></li> <li><a class="mw-selflink selflink">von Helmholtz</a></li> <li><a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">Joule</a></li> <li><a href="/wiki/Lord_Kelvin" title="Lord Kelvin">Kelvin</a></li> <li><a href="/wiki/Gilbert_N._Lewis" title="Gilbert N. Lewis">Lewis</a></li> <li><a href="/wiki/Fran%C3%A7ois_Massieu" title="François Massieu">Massieu</a></li> <li><a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a></li> <li><a href="/wiki/Julius_von_Mayer" title="Julius von Mayer">von Mayer</a></li> <li><a href="/wiki/Walther_Nernst" title="Walther Nernst">Nernst</a></li> <li><a href="/wiki/Lars_Onsager" title="Lars Onsager">Onsager</a></li> <li><a href="/wiki/Max_Planck" title="Max Planck">Planck</a></li> <li><a href="/wiki/William_John_Macquorn_Rankine" class="mw-redirect" title="William John Macquorn Rankine">Rankine</a></li> <li><a href="/wiki/John_Smeaton" title="John Smeaton">Smeaton</a></li> <li><a href="/wiki/Georg_Ernst_Stahl" title="Georg Ernst Stahl">Stahl</a></li> <li><a href="/wiki/Peter_Tait_(physicist)" class="mw-redirect" title="Peter Tait (physicist)">Tait</a></li> <li><a href="/wiki/Benjamin_Thompson" title="Benjamin Thompson">Thompson</a></li> <li><a href="/wiki/Johannes_Diderik_van_der_Waals" title="Johannes Diderik van der Waals">van der Waals</a></li> <li><a href="/wiki/John_James_Waterston" title="John James Waterston">Waterston</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf;;color: var(--color-base)"><div class="sidebar-list-title-c">Other</div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Nucleation" title="Nucleation">Nucleation</a></li> <li><a href="/wiki/Self-assembly" title="Self-assembly">Self-assembly</a></li> <li><a href="/wiki/Self-organization" title="Self-organization">Self-organization</a></li> <li><a href="/wiki/Order_and_disorder" title="Order and disorder">Order and disorder</a></li></ul></div></div></td> </tr><tr><td class="sidebar-below"> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" 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href="/wiki/Template:Thermodynamics_sidebar" title="Template:Thermodynamics sidebar"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Thermodynamics_sidebar" title="Template talk:Thermodynamics sidebar"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Thermodynamics_sidebar" title="Special:EditPage/Template:Thermodynamics sidebar"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Helmholtz%27s_polyphonic_siren,_Hunterian_Museum,_Glasgow.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Helmholtz%27s_polyphonic_siren%2C_Hunterian_Museum%2C_Glasgow.jpg/220px-Helmholtz%27s_polyphonic_siren%2C_Hunterian_Museum%2C_Glasgow.jpg" decoding="async" width="220" height="330" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Helmholtz%27s_polyphonic_siren%2C_Hunterian_Museum%2C_Glasgow.jpg/330px-Helmholtz%27s_polyphonic_siren%2C_Hunterian_Museum%2C_Glasgow.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Helmholtz%27s_polyphonic_siren%2C_Hunterian_Museum%2C_Glasgow.jpg/440px-Helmholtz%27s_polyphonic_siren%2C_Hunterian_Museum%2C_Glasgow.jpg 2x" data-file-width="2056" data-file-height="3088" /></a><figcaption>Helmholtz's polyphonic siren, Hunterian Museum, Glasgow</figcaption></figure> <p><b>Hermann Ludwig Ferdinand von Helmholtz</b> (<span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt" lang="en-fonipa"><a href="/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="/ˈ/: primary stress follows">ˈ</span><span title="'h' in 'hi'">h</span><span title="/ɛ/: 'e' in 'dress'">ɛ</span><span title="'l' in 'lie'">l</span><span title="'m' in 'my'">m</span><span title="'h' in 'hi'">h</span><span title="/oʊ/: 'o' in 'code'">oʊ</span><span title="'l' in 'lie'">l</span><span title="'t' in 'tie'">t</span><span title="'s' in 'sigh'">s</span></span>/</a></span></span>; <style data-mw-deduplicate="TemplateStyles:r1177148991">.mw-parser-output .IPA-label-small{font-size:85%}.mw-parser-output .references .IPA-label-small,.mw-parser-output .infobox .IPA-label-small,.mw-parser-output .navbox .IPA-label-small{font-size:100%}</style><span class="IPA-label IPA-label-small">German:</span> <span class="IPA nowrap" lang="de-Latn-fonipa"><a href="/wiki/Help:IPA/Standard_German" title="Help:IPA/Standard German">[ˈhɛʁ.man<span class="wrap"> </span>vɔn<span class="wrap"> </span>ˈhɛlmˌhɔlts]</a></span>; 31 August 1821 – 8 September 1894; "von" since 1883) was a German <a href="/wiki/Physicist" title="Physicist">physicist</a> and <a href="/wiki/Physician" title="Physician">physician</a> who made significant contributions in several scientific fields, particularly <a href="/wiki/Hydrodynamic_stability" title="Hydrodynamic stability">hydrodynamic stability</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Helmholtz_Association_of_German_Research_Centres" class="mw-redirect" title="Helmholtz Association of German Research Centres">Helmholtz Association</a>, the largest German association of <a href="/wiki/Research_institution" class="mw-redirect" title="Research institution">research institutions</a>, was named in his honour.<sup id="cite_ref-Gemeinschaft_3-0" class="reference"><a href="#cite_note-Gemeinschaft-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>In the fields of <a href="/wiki/Physiology" title="Physiology">physiology</a> and <a href="/wiki/Psychology" title="Psychology">psychology</a>, Helmholtz is known for his mathematics concerning the <a href="/wiki/Human_eye" title="Human eye">eye</a>, <a href="/wiki/Theory_of_vision" class="mw-redirect" title="Theory of vision">theories of vision</a>, ideas on the <a href="/wiki/Visual_perception" title="Visual perception">visual perception</a> of space, <a href="/wiki/Colour_vision" class="mw-redirect" title="Colour vision">colour vision</a> research, the sensation of tone, perceptions of sound, and <a href="/wiki/Empiricism" title="Empiricism">empiricism</a> in the physiology of perception. In <a href="/wiki/Physics" title="Physics">physics</a>, he is known for his theories on the conservation of <a href="/wiki/Energy" title="Energy">energy</a> and on the electrical <a href="/wiki/Double_layer_(surface_science)" title="Double layer (surface science)">double layer</a>, work in <a href="/wiki/Electrodynamics" class="mw-redirect" title="Electrodynamics">electrodynamics</a>, <a href="/wiki/Chemical_thermodynamics" title="Chemical thermodynamics">chemical thermodynamics</a>, and on a <a href="/wiki/Mechanics" title="Mechanics">mechanical</a> foundation of <a href="/wiki/Thermodynamics" title="Thermodynamics">thermodynamics</a>. Although credit is shared with <a href="/wiki/Julius_von_Mayer" title="Julius von Mayer">Julius von Mayer</a>, <a href="/wiki/James_Joule" class="mw-redirect" title="James Joule">James Joule</a>, and <a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Daniel Bernoulli</a>—among others—for the energy conservation principles that eventually led to the <a href="/wiki/First_law_of_thermodynamics" title="First law of thermodynamics">first law of thermodynamics</a>, he is credited with the first formulation of the energy conservation principle in its maximally general form.<sup id="cite_ref-Patton_4-0" class="reference"><a href="#cite_note-Patton-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>As a <a href="/wiki/Philosopher" class="mw-redirect" title="Philosopher">philosopher</a>, he is known for his <a href="/wiki/Philosophy_of_science" title="Philosophy of science">philosophy of science</a>, ideas on the relation between the laws of perception and the <a href="/wiki/Physical_law" class="mw-redirect" title="Physical law">laws of nature</a>, the science of <a href="/wiki/Aesthetics" title="Aesthetics">aesthetics</a>, and ideas on the civilizing power of science. By the late nineteenth century, Helmholtz's development of a broadly Kantian methodology, including the <i>a priori</i> determination of the manifold of possible orientations in perceptual space, had inspired new readings of Kant<sup id="cite_ref-Patton_4-1" class="reference"><a href="#cite_note-Patton-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> and contributed to the late modern <a href="/wiki/Neo-Kantianism" title="Neo-Kantianism">neo-Kantianism</a> movement in philosophy.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Biography">Biography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=1" title="Edit section: Biography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Early_years">Early years</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=2" title="Edit section: Early years"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Helmholtz was born in <a href="/wiki/Potsdam" title="Potsdam">Potsdam</a>, the son of the local <a href="/wiki/Gymnasium_(school)" title="Gymnasium (school)">gymnasium</a> headmaster, Ferdinand Helmholtz, who had studied <a href="/wiki/Classical_philology" class="mw-redirect" title="Classical philology">classical philology</a> and <a href="/wiki/Philosophy" title="Philosophy">philosophy</a>, and who was a close friend of the publisher and philosopher <a href="/wiki/Immanuel_Hermann_Fichte" title="Immanuel Hermann Fichte">Immanuel Hermann Fichte</a>. Helmholtz's work was influenced by the philosophy of <a href="/wiki/Johann_Gottlieb_Fichte" title="Johann Gottlieb Fichte">Johann Gottlieb Fichte</a> and <a href="/wiki/Immanuel_Kant" title="Immanuel Kant">Immanuel Kant</a>. He tried to trace their theories in empirical matters like <a href="/wiki/Physiology" title="Physiology">physiology</a>. </p><p>As a young man, Helmholtz was interested in natural science, but his father wanted him to study medicine. Helmholtz earned a <a href="/wiki/Medical_doctorate" class="mw-redirect" title="Medical doctorate">medical doctorate</a> at Medizinisch-chirurgisches Friedrich-Wilhelm-Institute in 1842 and served a one-year internship at the <a href="/wiki/Charit%C3%A9" title="Charité">Charité</a> hospital<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> (because there was financial support for medical students). </p><p>Trained primarily in physiology, Helmholtz wrote on many other topics, ranging from theoretical physics to the <a href="/wiki/Age_of_the_Earth" class="mw-redirect" title="Age of the Earth">age of the Earth</a>, and to the origin of the <a href="/wiki/Solar_System" title="Solar System">Solar System</a>. </p> <div class="mw-heading mw-heading3"><h3 id="University_posts">University posts</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=3" title="Edit section: University posts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Helmholtz's first academic position was as a teacher of anatomy at the Academy of Arts in Berlin in 1848.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> He then moved to take a post of associate professor of physiology at the Prussian <a href="/wiki/University_of_K%C3%B6nigsberg" title="University of Königsberg">University of Königsberg</a>, where he was appointed in 1849. In 1855 he accepted a full professorship of anatomy and physiology at the <a href="/wiki/University_of_Bonn" title="University of Bonn">University of Bonn</a>. He was not particularly happy in Bonn, however, and three years later he transferred to the <a href="/wiki/University_of_Heidelberg" class="mw-redirect" title="University of Heidelberg">University of Heidelberg</a>, in <a href="/wiki/Baden" title="Baden">Baden</a>, where he served as professor of physiology. In 1871 he accepted his final university position, as professor of physics at the <a href="/wiki/Humboldt_University_of_Berlin" title="Humboldt University of Berlin">Friedrich Wilhelm University</a> in Berlin. </p> <div class="mw-heading mw-heading2"><h2 id="Research">Research</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=4" title="Edit section: Research"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Helmholtz_1848.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Helmholtz_1848.jpg/170px-Helmholtz_1848.jpg" decoding="async" width="170" height="219" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Helmholtz_1848.jpg/255px-Helmholtz_1848.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/06/Helmholtz_1848.jpg/340px-Helmholtz_1848.jpg 2x" data-file-width="683" data-file-height="879" /></a><figcaption>Helmholtz in 1848</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Mechanics">Mechanics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=5" title="Edit section: Mechanics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>His first important scientific achievement, an 1847 treatise on the <a href="/wiki/Conservation_of_energy" title="Conservation of energy">conservation of energy</a>, was written in the context of his medical studies and philosophical background. His work on energy conservation came about while studying <a href="/wiki/Muscle" title="Muscle">muscle</a> <a href="/wiki/Metabolism" title="Metabolism">metabolism</a>. He tried to demonstrate that no energy is lost in muscle movement, motivated by the implication that there were no <i>vital forces</i> necessary to move a muscle. This was a rejection of the speculative tradition of <i><a href="/wiki/Naturphilosophie" title="Naturphilosophie">Naturphilosophie</a></i> and <a href="/wiki/Vitalism" title="Vitalism">vitalism</a> which was at that time a dominant philosophical paradigm in German physiology. He was working against the argument, promoted by some vitalists, that "living force" can power a machine indefinitely.<sup id="cite_ref-Patton_4-2" class="reference"><a href="#cite_note-Patton-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Drawing on the earlier work of <a href="/wiki/Nicolas_L%C3%A9onard_Sadi_Carnot" title="Nicolas Léonard Sadi Carnot">Sadi Carnot</a>, <a href="/wiki/Beno%C3%AEt_Paul_%C3%89mile_Clapeyron" class="mw-redirect" title="Benoît Paul Émile Clapeyron">Benoît Paul Émile Clapeyron</a> and <a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">James Prescott Joule</a>, he postulated a relationship between <a href="/wiki/Mechanics" title="Mechanics">mechanics</a>, <a href="/wiki/Heat" title="Heat">heat</a>, <a href="/wiki/Light" title="Light">light</a>, <a href="/wiki/Electricity" title="Electricity">electricity</a> and <a href="/wiki/Magnetism" title="Magnetism">magnetism</a> by treating them all as manifestations of a single <i>force</i>, or <a href="/wiki/Energy" title="Energy">energy</a> in today's terminology. He published his theories in his book <i>Über die Erhaltung der Kraft</i> (<i>On the Conservation of Force</i>, 1847).<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>In the 1850s and 60s, building on the publications of <a href="/wiki/William_Thomson,_1st_Baron_Kelvin" class="mw-redirect" title="William Thomson, 1st Baron Kelvin">William Thomson</a>, Helmholtz and <a href="/wiki/William_Rankine" title="William Rankine">William Rankine</a> helped popularize the idea of the <a href="/wiki/Heat_death_of_the_universe" title="Heat death of the universe">heat death of the universe</a>. </p><p> In fluid dynamics, Helmholtz made several contributions, including <a href="/wiki/Helmholtz%27s_theorems" title="Helmholtz's theorems">Helmholtz's theorems</a> for vortex dynamics in inviscid fluids.</p><ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Helmholtz-1.jpg" class="mw-file-description" title="1889 copy of Helmholtz's "Über die Erhaltung der Kraft", no. 1"><img alt="1889 copy of Helmholtz's "Über die Erhaltung der Kraft", no. 1" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Helmholtz-1.jpg/75px-Helmholtz-1.jpg" decoding="async" width="75" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Helmholtz-1.jpg/112px-Helmholtz-1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/55/Helmholtz-1.jpg/150px-Helmholtz-1.jpg 2x" data-file-width="2354" data-file-height="3764" /></a></span></div> <div class="gallerytext">1889 copy of Helmholtz's "Über die Erhaltung der Kraft", no. 1</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Helmholtz-2.jpg" class="mw-file-description" title="Title page of "Über die Erhaltung der Kraft", no. 1"><img alt="Title page of "Über die Erhaltung der Kraft", no. 1" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Helmholtz-2.jpg/77px-Helmholtz-2.jpg" decoding="async" width="77" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Helmholtz-2.jpg/116px-Helmholtz-2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Helmholtz-2.jpg/154px-Helmholtz-2.jpg 2x" data-file-width="2490" data-file-height="3867" /></a></span></div> <div class="gallerytext">Title page of "Über die Erhaltung der Kraft", no. 1</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Helmholtz-3.jpg" class="mw-file-description" title="First page of "Über die Erhaltung der Kraft", no. 1"><img alt="First page of "Über die Erhaltung der Kraft", no. 1" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Helmholtz-3.jpg/73px-Helmholtz-3.jpg" decoding="async" width="73" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Helmholtz-3.jpg/110px-Helmholtz-3.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Helmholtz-3.jpg/147px-Helmholtz-3.jpg 2x" data-file-width="2381" data-file-height="3887" /></a></span></div> <div class="gallerytext">First page of "Über die Erhaltung der Kraft", no. 1</div> </li> </ul> <div class="mw-heading mw-heading3"><h3 id="Sensory_physiology">Sensory physiology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=6" title="Edit section: Sensory physiology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Helmholtz was a pioneer in the scientific study of human vision and audition. Inspired by <a href="/wiki/Psychophysics" title="Psychophysics">psychophysics</a>, 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". </p><p>The sensory physiology of Helmholtz was the basis of the work of <a href="/wiki/Wilhelm_Wundt" title="Wilhelm Wundt">Wilhelm Wundt</a>, a student of Helmholtz, who is considered one of the founders of experimental <a href="/wiki/Psychology" title="Psychology">psychology</a>. 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 <a href="/wiki/Naturphilosophie" title="Naturphilosophie">Naturphilosophie</a>, stressed the importance of <a href="/wiki/Materialism" title="Materialism">materialism</a>, and was focusing more on the unity of "mind" and body.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Ophthalmic_optics">Ophthalmic optics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=7" title="Edit section: Ophthalmic optics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1851, Helmholtz revolutionized the field of <a href="/wiki/Ophthalmology" title="Ophthalmology">ophthalmology</a> with the invention of the <a href="/wiki/Ophthalmoscope" class="mw-redirect" title="Ophthalmoscope">ophthalmoscope</a>; an instrument used to examine the inside of the <a href="/wiki/Human_eye" title="Human eye">human eye</a>. 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 <i>Handbuch der Physiologischen Optik</i> (<i>Handbook of Physiological Optics</i> or <i>Treatise on Physiological Optics</i>; English translation of the 3rd volume <a rel="nofollow" class="external text" href="https://web.archive.org/web/20180320133752/http://poseidon.sunyopt.edu/BackusLab/Helmholtz/">here</a>), provided empirical theories on <a href="/wiki/Depth_perception" title="Depth perception">depth perception</a>, <a href="/wiki/Colour_vision" class="mw-redirect" title="Colour vision">colour vision</a>, and <a href="/wiki/Motion_perception" title="Motion perception">motion perception</a>, 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 <a href="/wiki/Unconscious_inference" title="Unconscious inference">unconscious inferences</a> for perception. The <i>Handbuch</i> was first translated into English under the editorship of <a href="/wiki/James_P._C._Southall" title="James P. C. Southall">James P. C. Southall</a> on behalf of the <a href="/wiki/Optical_Society_of_America" class="mw-redirect" title="Optical Society of America">Optical Society of America</a> in 1924–5. His theory of <a href="/wiki/Accommodation_reflex" title="Accommodation reflex">accommodation</a> went unchallenged until the final decade of the 20th century. </p><p>Helmholtz continued to work for several decades on several editions of the handbook, frequently updating his work because of his dispute with <a href="/wiki/Ewald_Hering" title="Ewald Hering">Ewald Hering</a> who held opposite views on spatial and colour vision. This dispute divided the discipline of physiology during the second half of the 1800s. </p> <div class="mw-heading mw-heading3"><h3 id="Nerve_physiology">Nerve physiology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=8" title="Edit section: Nerve physiology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>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.<sup id="cite_ref-glynn_10-0" class="reference"><a href="#cite_note-glynn-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> He used a recently dissected sciatic nerve of a frog and the calf muscle to which it attached. He used a <a href="/wiki/Galvanometer" title="Galvanometer">galvanometer</a> 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.<sup id="cite_ref-glynn_10-1" class="reference"><a href="#cite_note-glynn-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Helmholtz reported<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> transmission speeds in the range of 24.6 – 38.4 meters per second.<sup id="cite_ref-glynn_10-2" class="reference"><a href="#cite_note-glynn-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Acoustics_and_aesthetics">Acoustics and aesthetics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=9" title="Edit section: Acoustics and aesthetics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Hermann_von_Helmholtz-2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Hermann_von_Helmholtz-2.jpg/220px-Hermann_von_Helmholtz-2.jpg" decoding="async" width="220" height="410" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Hermann_von_Helmholtz-2.jpg/330px-Hermann_von_Helmholtz-2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Hermann_von_Helmholtz-2.jpg/440px-Hermann_von_Helmholtz-2.jpg 2x" data-file-width="2422" data-file-height="4519" /></a><figcaption>Last photograph of von Helmholtz, taken three days before his final illness</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Helmholtz_resonator_2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Helmholtz_resonator_2.jpg/220px-Helmholtz_resonator_2.jpg" decoding="async" width="220" height="167" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Helmholtz_resonator_2.jpg/330px-Helmholtz_resonator_2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Helmholtz_resonator_2.jpg/440px-Helmholtz_resonator_2.jpg 2x" data-file-width="665" data-file-height="504" /></a><figcaption>The Helmholtz resonator (<i>i</i>) and instrumentation</figcaption></figure> <p>In 1863, Helmholtz published <i><a href="/wiki/Sensations_of_Tone" title="Sensations of Tone">Sensations of Tone</a></i>, once again demonstrating his interest in the physics of perception. This book influenced musicologists into the twentieth century. Helmholtz invented the <a href="/wiki/Helmholtz_resonance" title="Helmholtz resonance">Helmholtz resonator</a> to identify the various <a href="/wiki/Audio_frequency" title="Audio frequency">frequencies</a> or <a href="/wiki/Pitch_(music)" title="Pitch (music)">pitches</a> of the pure <a href="/wiki/Sine_wave" title="Sine wave">sine wave</a> components of <a href="/wiki/Fourier_analysis#Applications_in_signal_processing" title="Fourier analysis">complex sounds containing multiple tones</a>.<sup id="cite_ref-Helmholtz1885_13-0" class="reference"><a href="#cite_note-Helmholtz1885-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>Helmholtz showed that different combinations of resonators could mimic <a href="/wiki/Vowel" title="Vowel">vowel</a> sounds: <a href="/wiki/Alexander_Graham_Bell" title="Alexander Graham Bell">Alexander Graham Bell</a> in particular was interested in this but, not being able to read German, misconstrued Helmholtz's 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 <a href="/wiki/Harmonic_telegraph" class="mw-redirect" title="Harmonic telegraph">harmonic telegraph</a> principle.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-MacKenzie2008_15-0" class="reference"><a href="#cite_note-MacKenzie2008-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Ludwig_Knaus_-_Der_Physiker_Hermann_von_Helmholtz_(1881).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Ludwig_Knaus_-_Der_Physiker_Hermann_von_Helmholtz_%281881%29.jpg/170px-Ludwig_Knaus_-_Der_Physiker_Hermann_von_Helmholtz_%281881%29.jpg" decoding="async" width="170" height="243" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Ludwig_Knaus_-_Der_Physiker_Hermann_von_Helmholtz_%281881%29.jpg/255px-Ludwig_Knaus_-_Der_Physiker_Hermann_von_Helmholtz_%281881%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Ludwig_Knaus_-_Der_Physiker_Hermann_von_Helmholtz_%281881%29.jpg/340px-Ludwig_Knaus_-_Der_Physiker_Hermann_von_Helmholtz_%281881%29.jpg 2x" data-file-width="2311" data-file-height="3303" /></a><figcaption>Helmholtz in 1881, portrait by <a href="/wiki/Ludwig_Knaus" title="Ludwig Knaus">Ludwig Knaus</a></figcaption></figure> <p>The translation by <a href="/wiki/Alexander_J._Ellis" class="mw-redirect" title="Alexander J. Ellis">Alexander J. Ellis</a> 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).<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Electromagnetism">Electromagnetism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=10" title="Edit section: Electromagnetism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Helmholtz studied electrical oscillations from 1869 to 1871, and in a lecture delivered to the Naturhistorisch-medizinischen Verein zu Heidelberg (Natural History and Medical Association of Heidelberg) on 30 April 1869, titled <i>On Electrical Oscillations</i>, he indicated that the perceptible damped electrical oscillations in a coil connected to a <a href="/wiki/Leyden_jar" title="Leyden jar">Leyden jar</a> were about <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac"><span class="num">1</span>⁄<span class="den">50</span></span> second in duration.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>In 1871, Helmholtz moved from Heidelberg to Berlin to become a professor of physics. He became interested in <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a>, and the <a href="/wiki/Helmholtz_equation" title="Helmholtz equation">Helmholtz equation</a> is named for him. Although he made no major contributions to this field, his student <a href="/wiki/Heinrich_Rudolf_Hertz" class="mw-redirect" title="Heinrich Rudolf Hertz">Heinrich Rudolf Hertz</a> became famous as the first to demonstrate <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a>. <a href="/wiki/Oliver_Heaviside" title="Oliver Heaviside">Oliver Heaviside</a> criticised Helmholtz's electromagnetic theory because it allowed the existence of <a href="/wiki/Longitudinal_wave" title="Longitudinal wave">longitudinal waves</a>. Based on work on <a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a>, 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.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Philosophy">Philosophy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=11" title="Edit section: Philosophy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Helmholtz' scientific work in physiology and mechanics occasioned much that he is known for in <a href="/wiki/Philosophy_of_science" title="Philosophy of science">philosophy of science</a>, including ideas on the relation between the laws of perception and the <a href="/wiki/Physical_law" class="mw-redirect" title="Physical law">laws of nature</a> and his rejection of the exclusive use of <a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean geometry</a>.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p><p>His philosophy of science wavered between some version of <a href="/wiki/Empiricism" title="Empiricism">empiricism</a> and <a href="/wiki/Transcendentalism" title="Transcendentalism">transcendentalism</a>.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> Despite the speculative associations of the latter, his philosophy of science is thoroughly indebted to his use of mathematical physics to supplant vitalism and articulate the general conservation of energy principle.<sup id="cite_ref-Patton_4-3" class="reference"><a href="#cite_note-Patton-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>His rejection of Euclidean geometry as the only possible science of space is central to understanding his appropriation of Kant's philosophy of space, which ostensibly requires Euclidean geometry to be that exclusive <i>a priori</i> science of <a href="/wiki/Physical_space" class="mw-redirect" title="Physical space">physical space</a>. Helmholtz introduced a new conception of the <i>a priori</i> in space: that of the determination of the manifold of possible orientations in perceptual space. These developments inspired new readings of Kant<sup id="cite_ref-Patton_4-4" class="reference"><a href="#cite_note-Patton-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> and contributed to the rise of late modern <a href="/wiki/Neo-Kantianism" title="Neo-Kantianism">neo-Kantianism</a> movement in philosophy. </p> <div class="mw-heading mw-heading2"><h2 id="Students_and_associates">Students and associates</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=12" title="Edit section: Students and associates"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Other students and research associates of Helmholtz at Berlin included <a href="/wiki/Max_Planck" title="Max Planck">Max Planck</a>, <a href="/wiki/Heinrich_Kayser" title="Heinrich Kayser">Heinrich Kayser</a>, <a href="/wiki/Eugen_Goldstein" title="Eugen Goldstein">Eugen Goldstein</a>, <a href="/wiki/Wilhelm_Wien" title="Wilhelm Wien">Wilhelm Wien</a>, <a href="/wiki/Arthur_K%C3%B6nig" title="Arthur König">Arthur König</a>, <a href="/wiki/Henry_Augustus_Rowland" title="Henry Augustus Rowland">Henry Augustus Rowland</a>, <a href="/wiki/Albert_A._Michelson" title="Albert A. Michelson">Albert A. Michelson</a>, <a href="/wiki/Wilhelm_Wundt" title="Wilhelm Wundt">Wilhelm Wundt</a>, <a href="/wiki/Fernando_Sanford" title="Fernando Sanford">Fernando Sanford</a> and <a href="/wiki/Michael_I._Pupin" class="mw-redirect" title="Michael I. Pupin">Michael I. Pupin</a>. <a href="/wiki/Leo_Koenigsberger" class="mw-redirect" title="Leo Koenigsberger">Leo Koenigsberger</a>, who was his colleague from 1869 to 1871 in Heidelberg, wrote the definitive biography of him in 1902. </p> <div class="mw-heading mw-heading2"><h2 id="Honours_and_legacy">Honours and legacy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=13" title="Edit section: Honours and legacy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Hermann_von_Helmholtz-Statue_vor_der_Humboldt-Universit%C3%A4t_zu_Berlin.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Hermann_von_Helmholtz-Statue_vor_der_Humboldt-Universit%C3%A4t_zu_Berlin.jpg/170px-Hermann_von_Helmholtz-Statue_vor_der_Humboldt-Universit%C3%A4t_zu_Berlin.jpg" decoding="async" width="170" height="269" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Hermann_von_Helmholtz-Statue_vor_der_Humboldt-Universit%C3%A4t_zu_Berlin.jpg/255px-Hermann_von_Helmholtz-Statue_vor_der_Humboldt-Universit%C3%A4t_zu_Berlin.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Hermann_von_Helmholtz-Statue_vor_der_Humboldt-Universit%C3%A4t_zu_Berlin.jpg/340px-Hermann_von_Helmholtz-Statue_vor_der_Humboldt-Universit%C3%A4t_zu_Berlin.jpg 2x" data-file-width="2529" data-file-height="4000" /></a><figcaption>Helmholtz's statue in front of Humboldt University in Berlin</figcaption></figure> <ul><li>In 1873, Helmholtz was elected as a member of the <a href="/wiki/American_Philosophical_Society" title="American Philosophical Society">American Philosophical Society</a>.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup></li> <li>In 1881, Helmholtz was elected <a href="/wiki/Fellowship_of_the_Royal_College_of_Surgeons" class="mw-redirect" title="Fellowship of the Royal College of Surgeons">Honorary Fellow</a> of the <a href="/wiki/Royal_College_of_Surgeons_in_Ireland" title="Royal College of Surgeons in Ireland">Royal College of Surgeons in Ireland</a>.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup></li> <li>On 10 November 1881, he was awarded the <a href="/wiki/Legion_of_Honour" title="Legion of Honour">Légion d'honneur</a>: au grade de Commandeur, or Level 3 – a senior grade. (No. 2173).</li> <li>In 1883, Professor Helmholtz was honoured by the Emperor, being raised to the nobility, or <i>Adel</i>. The <i>Adelung</i> meant that he and his family were now styled: <b>von</b> Helmholtz. The distinction was not a peerage or title, but it was hereditary and conferred a certain social cachet.</li> <li>Helmholtz was conferred the Honorary Membership of the <a href="/wiki/Institution_of_Engineers_and_Shipbuilders_in_Scotland" class="mw-redirect" title="Institution of Engineers and Shipbuilders in Scotland">Institution of Engineers and Shipbuilders in Scotland</a> in 1884.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup></li> <li>The largest German association of <a href="/wiki/Research_institution" class="mw-redirect" title="Research institution">research institutions</a>, the <a href="/wiki/Helmholtz_Association_of_German_Research_Centres" class="mw-redirect" title="Helmholtz Association of German Research Centres">Helmholtz Association</a>, is named after him.<sup id="cite_ref-Gemeinschaft_3-1" class="reference"><a href="#cite_note-Gemeinschaft-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-History_26-0" class="reference"><a href="#cite_note-History-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup></li> <li>The asteroid <a href="/wiki/11573_Helmholtz" title="11573 Helmholtz">11573 Helmholtz</a> and the lunar crater <i><a href="/wiki/Helmholtz_(lunar_crater)" title="Helmholtz (lunar crater)">Helmholtz</a></i> as well as the crater <i><a href="/wiki/Helmholtz_(Martian_crater)" class="mw-redirect" title="Helmholtz (Martian crater)">Helmholtz</a></i> on Mars were named in his honour.<sup id="cite_ref-Asteroid_27-0" class="reference"><a href="#cite_note-Asteroid-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup></li> <li>In <a href="/wiki/Charlottenburg" title="Charlottenburg">Charlottenburg</a>, <a href="/wiki/Berlin" title="Berlin">Berlin</a>, the street <i>Helmholtzstraße</i> is named after von Helmholtz.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup></li></ul> <style data-mw-deduplicate="TemplateStyles:r1273380762/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti 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srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/French_Presidential_Decree_-Award_of_Legion_of_Honour_to_Helholtz%2C_Bell_and_Edison_-10_November_1881_Pg._1.jpg/240px-French_Presidential_Decree_-Award_of_Legion_of_Honour_to_Helholtz%2C_Bell_and_Edison_-10_November_1881_Pg._1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c5/French_Presidential_Decree_-Award_of_Legion_of_Honour_to_Helholtz%2C_Bell_and_Edison_-10_November_1881_Pg._1.jpg/320px-French_Presidential_Decree_-Award_of_Legion_of_Honour_to_Helholtz%2C_Bell_and_Edison_-10_November_1881_Pg._1.jpg 2x" data-file-width="2496" data-file-height="3480" /></a></span></div></div><div class="tsingle" style="width:162px;max-width:162px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:French_Presidential_Decree_-Award_of_Legion_of_Honour_to_Helholtz,_Bell_and_Edison_-10_November_1881_Pg._3.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/French_Presidential_Decree_-Award_of_Legion_of_Honour_to_Helholtz%2C_Bell_and_Edison_-10_November_1881_Pg._3.jpg/160px-French_Presidential_Decree_-Award_of_Legion_of_Honour_to_Helholtz%2C_Bell_and_Edison_-10_November_1881_Pg._3.jpg" decoding="async" width="160" height="218" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/French_Presidential_Decree_-Award_of_Legion_of_Honour_to_Helholtz%2C_Bell_and_Edison_-10_November_1881_Pg._3.jpg/240px-French_Presidential_Decree_-Award_of_Legion_of_Honour_to_Helholtz%2C_Bell_and_Edison_-10_November_1881_Pg._3.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bf/French_Presidential_Decree_-Award_of_Legion_of_Honour_to_Helholtz%2C_Bell_and_Edison_-10_November_1881_Pg._3.jpg/320px-French_Presidential_Decree_-Award_of_Legion_of_Honour_to_Helholtz%2C_Bell_and_Edison_-10_November_1881_Pg._3.jpg 2x" data-file-width="2454" data-file-height="3336" /></a></span></div></div><div class="tsingle" style="width:138px;max-width:138px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:French_Presidential_Decree_-Award_of_Legion_of_Honour_to_Helholtz,_Bell_and_Edison_-10_November_1881_Pg._5.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c0/French_Presidential_Decree_-Award_of_Legion_of_Honour_to_Helholtz%2C_Bell_and_Edison_-10_November_1881_Pg._5.jpg/136px-French_Presidential_Decree_-Award_of_Legion_of_Honour_to_Helholtz%2C_Bell_and_Edison_-10_November_1881_Pg._5.jpg" decoding="async" width="136" height="218" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c0/French_Presidential_Decree_-Award_of_Legion_of_Honour_to_Helholtz%2C_Bell_and_Edison_-10_November_1881_Pg._5.jpg/204px-French_Presidential_Decree_-Award_of_Legion_of_Honour_to_Helholtz%2C_Bell_and_Edison_-10_November_1881_Pg._5.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c0/French_Presidential_Decree_-Award_of_Legion_of_Honour_to_Helholtz%2C_Bell_and_Edison_-10_November_1881_Pg._5.jpg/272px-French_Presidential_Decree_-Award_of_Legion_of_Honour_to_Helholtz%2C_Bell_and_Edison_-10_November_1881_Pg._5.jpg 2x" data-file-width="2058" data-file-height="3294" /></a></span></div></div></div><div class="trow" style="display:flex"><div class="thumbcaption">Decree awarding Helmholtz (listed in first page) the <a href="/wiki/French_Legion_of_Honour" class="mw-redirect" title="French Legion of Honour">French Legion of Honour</a></div></div></div></div> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading2"><h2 id="Works">Works</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=14" title="Edit section: Works"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=6555455"><i>Über die Erhaltung der Kraft</i></a> (in German). Leipzig: Wilhelm Engelmann. 1889.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%C3%9Cber+die+Erhaltung+der+Kraft&rft.place=Leipzig&rft.pub=Wilhelm+Engelmann&rft.date=1889&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D6555455&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=6723936"><i>Vorlesungen über die elektromagnetische Theorie des Lichts</i></a> (in German). Leipzig: Johann Ambrosius Barth. 1897.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Vorlesungen+%C3%BCber+die+elektromagnetische+Theorie+des+Lichts&rft.place=Leipzig&rft.pub=Johann+Ambrosius+Barth&rft.date=1897&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D6723936&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=6725127"><i>Vorlesungen über die mathematischen Principien der Akustik</i></a> (in German). Leipzig: Johann Ambrosius Barth. 1898.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Vorlesungen+%C3%BCber+die+mathematischen+Principien+der+Akustik&rft.place=Leipzig&rft.pub=Johann+Ambrosius+Barth&rft.date=1898&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D6725127&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=6725946"><i>Vorlesungen über die Dynamik discreter Massenpunkte</i></a> (in German). Leipzig: Johann Ambrosius Barth. 1898.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Vorlesungen+%C3%BCber+die+Dynamik+discreter+Massenpunkte&rft.place=Leipzig&rft.pub=Johann+Ambrosius+Barth&rft.date=1898&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D6725946&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=6727137"><i>Dynamik continuirlich verbreiteter Massen</i></a> (in German). Leipzig: Johann Ambrosius Barth. 1902.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Dynamik+continuirlich+verbreiteter+Massen&rft.place=Leipzig&rft.pub=Johann+Ambrosius+Barth&rft.date=1902&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D6727137&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=7174058"><i>Vorlesungen über die Theorie der Wärme</i></a> (in German). Leipzig: Johann Ambrosius Barth. 1903.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Vorlesungen+%C3%BCber+die+Theorie+der+W%C3%A4rme&rft.place=Leipzig&rft.pub=Johann+Ambrosius+Barth&rft.date=1903&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D7174058&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=7174058"><i>Vorlesungen über Theoretische Physik</i></a> (in German). Leipzig: Johann Ambrosius Barth. 1903.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Vorlesungen+%C3%BCber+Theoretische+Physik&rft.place=Leipzig&rft.pub=Johann+Ambrosius+Barth&rft.date=1903&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D7174058&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading3"><h3 id="Translated_works">Translated works</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=15" title="Edit section: Translated works"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><i><a rel="nofollow" class="external text" href="https://books.google.com/books?id=C1i4AAAAIAAJ&pg=PA114">On the Conservation of Force</a></i> (1847) <a rel="nofollow" class="external text" href="http://hdl.handle.net/2027/uc1.b4252190?urlappend=%3Bseq=124">HathiTrust</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=6723591"><i>Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik</i></a> (in French). Paris: Masson. 1874.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Lehre+von+den+Tonempfindungen+als+physiologische+Grundlage+f%C3%BCr+die+Theorie+der+Musik&rft.place=Paris&rft.pub=Masson&rft.date=1874&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D6723591&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHelmholtz1876" class="citation journal cs1">Helmholtz, Herman (1876). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=-DE4AAAAMAAJ&q=optics%20limit%20abbe%20fripp&pg=PA15">"On the Limits of the Optical Capacity of the Microscope"</a>. <i>Monthly Microscopical Journal</i>. <b>16</b>: <span class="nowrap">15–</span>39. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1365-2818.1876.tb05606.x">10.1111/j.1365-2818.1876.tb05606.x</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Monthly+Microscopical+Journal&rft.atitle=On+the+Limits+of+the+Optical+Capacity+of+the+Microscope&rft.volume=16&rft.pages=%3Cspan+class%3D%22nowrap%22%3E15-%3C%2Fspan%3E39&rft.date=1876&rft_id=info%3Adoi%2F10.1111%2Fj.1365-2818.1876.tb05606.x&rft.aulast=Helmholtz&rft.aufirst=Herman&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D-DE4AAAAMAAJ%26q%3Doptics%2520limit%2520abbe%2520fripp%26pg%3DPA15&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://gutenberg.beic.it/webclient/DeliveryManager?pid=10984881"><i>Populäre wissenschaftliche Vorträge</i></a>. New York: Appleton. 1885.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Popul%C3%A4re+wissenschaftliche+Vortr%C3%A4ge&rft.place=New+York&rft.pub=Appleton&rft.date=1885&rft_id=https%3A%2F%2Fgutenberg.beic.it%2Fwebclient%2FDeliveryManager%3Fpid%3D10984881&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></li> <li><i><a rel="nofollow" class="external text" href="http://www.bartleby.com/30/125.html">On the Conservation of Force</a></i> (1895) Introduction to a Series of Lectures Delivered at <a href="/wiki/Karlsruhe" title="Karlsruhe">Carlsruhe</a> in the Winter of 1862–1863, English translation</li> <li><i><a rel="nofollow" class="external text" href="https://archive.org/details/onsensationsofto00helmrich">On the Sensations of Tone as a Physiological Basis for the Theory of Music</a></i> (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</li> <li><i><a rel="nofollow" class="external text" href="https://archive.org/details/onsensationston01helmgoog">On the Sensations of Tone as a Physiological Basis for the Theory of Music</a></i> (downloadable from Google Books) Fourth Edition, By Hermann von Helmholtz, Alexander John Ellis, Published by Longmans, Green, 1912, 575 pages</li> <li><i><a rel="nofollow" class="external text" href="https://web.archive.org/web/20180927064524/http://poseidon.sunyopt.edu/BackusLab/Helmholtz/">Treatise on Physiological Optics</a></i> (1910) three volumes. English translation by Optical Society of America (1924–25).</li> <li><i><a rel="nofollow" class="external text" href="https://archive.org/details/popularlectureso00helmuoft">Popular lectures on scientific subjects</a></i> (1885)</li> <li><i><a rel="nofollow" class="external text" href="https://archive.org/details/popularlectureso00helmrich">Popular lectures on scientific subjects</a></i> second series (1908)</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=16" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Helmholtz_coil" title="Helmholtz coil">Helmholtz coil</a></li> <li><a href="/wiki/List_of_people_from_Berlin" title="List of people from Berlin">List of people from Berlin</a></li> <li><a href="/wiki/List_of_things_named_after_Hermann_von_Helmholtz" title="List of things named after Hermann von Helmholtz">List of things named after Hermann von Helmholtz</a></li> <li><a href="/wiki/Neo-Kantianism" title="Neo-Kantianism">Neo-Kantianism</a></li> <li><a href="/wiki/Theory_of_Colours" title="Theory of Colours">Theory of Colours</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=17" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Citations">Citations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=18" title="Edit section: Citations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavid_Cahan1993" class="citation book cs1">David Cahan (1993). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Gx-ZGgeF2EwC&q=%22Johannes+von+Kries%22+psychologist&pg=PA198"><i>Hermann Von Helmholtz and the Foundations of Nineteenth-Century Science</i></a>. University of California Press. p. 198. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-520-08334-9" title="Special:BookSources/978-0-520-08334-9"><bdi>978-0-520-08334-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Hermann+Von+Helmholtz+and+the+Foundations+of+Nineteenth-Century+Science&rft.pages=198&rft.pub=University+of+California+Press&rft.date=1993&rft.isbn=978-0-520-08334-9&rft.au=David+Cahan&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DGx-ZGgeF2EwC%26q%3D%2522Johannes%2Bvon%2BKries%2522%2Bpsychologist%26pg%3DPA198&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBobba2004" class="citation thesis cs1">Bobba, Kumar Manoj (1 January 2004). <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2004PhDT.......158B"><i>Robust flow stability: Theory, computations and experiments in near-wall turbulence</i></a> (Thesis). <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2004PhDT.......158B">2004PhDT.......158B</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adissertation&rft.title=Robust+flow+stability%3A+Theory%2C+computations+and+experiments+in+near-wall+turbulence&rft.date=2004-01-01&rft_id=info%3Abibcode%2F2004PhDT.......158B&rft.aulast=Bobba&rft.aufirst=Kumar+Manoj&rft_id=https%3A%2F%2Fui.adsabs.harvard.edu%2Fabs%2F2004PhDT.......158B&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-Gemeinschaft-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Gemeinschaft_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Gemeinschaft_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.helmholtz.de/en/about-us/who-we-are/history/hermann-von-helmholtz/">"The polymath with a sense of practice"</a>. <i>Helmholtz-Gemeinschaft Deutscher Forschungszentren</i><span class="reference-accessdate">. Retrieved <span class="nowrap">4 October</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Helmholtz-Gemeinschaft+Deutscher+Forschungszentren&rft.atitle=The+polymath+with+a+sense+of+practice&rft_id=https%3A%2F%2Fwww.helmholtz.de%2Fen%2Fabout-us%2Fwho-we-are%2Fhistory%2Fhermann-von-helmholtz%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-Patton-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-Patton_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Patton_4-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Patton_4-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Patton_4-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Patton_4-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://plato.stanford.edu/entries/hermann-helmholtz/?simple=True">Patton, Lydia. "Hermann von Helmholtz." (2008), Stanford Encyclopedia of Philosophy.</a></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHeis2018" class="citation web cs1">Heis, Jeremy (2018). <a rel="nofollow" class="external text" href="https://plato.stanford.edu/entrieS/neo-kantianism/">"Neo-Kantianism"</a>. <i>Stanford Encyclopedia of Philosophy</i><span class="reference-accessdate">. Retrieved <span class="nowrap">6 October</span> 2024</span>. <q>This movement drew inspiration from a diverse cast of philosophers—principally, Kuno Fischer (Fischer 1860), Hermann von Helmholtz (Helmholtz 1867, 1878), Friedrich Lange (Lange 1866), Otto Liebmann (Liebmann 1865), and Eduard Zeller (Zeller 1862))—who in the middle of the nineteenth century were calling for a return to Kant's philosophy as an alternative to both speculative metaphysics and materialism (Beiser 2014b).</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Stanford+Encyclopedia+of+Philosophy&rft.atitle=Neo-Kantianism&rft.date=2018&rft.aulast=Heis&rft.aufirst=Jeremy&rft_id=https%3A%2F%2Fplato.stanford.edu%2FentrieS%2Fneo-kantianism%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">R. S. Turner, <i>In the Eye's Mind: Vision and the Helmholtz-Hering Controversy</i>, Princeton University Press, 2014, p. 36.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20130124115814/http://www.royalsoced.org.uk/cms/files/fellows/biographical_index/fells_indexp1.pdf"><i>Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002</i></a> <span class="cs1-format">(PDF)</span>. The Royal Society of Edinburgh. July 2006. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-902198-84-X" title="Special:BookSources/0-902198-84-X"><bdi>0-902198-84-X</bdi></a>. Archived from <a rel="nofollow" class="external text" href="https://www.royalsoced.org.uk/cms/files/fellows/biographical_index/fells_indexp1.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 24 January 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">21 October</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Biographical+Index+of+Former+Fellows+of+the+Royal+Society+of+Edinburgh+1783%E2%80%932002&rft.pub=The+Royal+Society+of+Edinburgh&rft.date=2006-07&rft.isbn=0-902198-84-X&rft_id=https%3A%2F%2Fwww.royalsoced.org.uk%2Fcms%2Ffiles%2Ffellows%2Fbiographical_index%2Ffells_indexp1.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">English translation published in <i>Scientific memoirs, selected from the transactions of foreign academies of science, and from foreign journals: Natural philosophy</i> (1853), p. 114; trans. by John Tyndall. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=C1i4AAAAIAAJ&pg=PA114">Google Books</a>, <a rel="nofollow" class="external text" href="http://hdl.handle.net/2027/uc1.b4252190?urlappend=%3Bseq=124">HathiTrust</a></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPeter_J._Bowler_and_Iwan_Rhys_Morus2005" class="citation book cs1">Peter J. Bowler and Iwan Rhys Morus (2005). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=LEl3s-wYg10C&q=Helmholtz+materialism++sensory+nineteenth-century+Naturphilosophie&pg=PA177"><i>Making Modern Science: A Historical Survey</i></a>. University of Chicago Press. p. 177. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-226-06861-9" title="Special:BookSources/978-0-226-06861-9"><bdi>978-0-226-06861-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Making+Modern+Science%3A+A+Historical+Survey&rft.pages=177&rft.pub=University+of+Chicago+Press&rft.date=2005&rft.isbn=978-0-226-06861-9&rft.au=Peter+J.+Bowler+and+Iwan+Rhys+Morus&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DLEl3s-wYg10C%26q%3DHelmholtz%2Bmaterialism%2B%2Bsensory%2Bnineteenth-century%2BNaturphilosophie%26pg%3DPA177&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-glynn-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-glynn_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-glynn_10-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-glynn_10-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGlynn2010" class="citation book cs1">Glynn, Ian (2010). <i>Elegance in Science</i>. Oxford: Oxford University Press. pp. <span class="nowrap">147–</span>150. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-957862-7" title="Special:BookSources/978-0-19-957862-7"><bdi>978-0-19-957862-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Elegance+in+Science&rft.place=Oxford&rft.pages=%3Cspan+class%3D%22nowrap%22%3E147-%3C%2Fspan%3E150&rft.pub=Oxford+University+Press&rft.date=2010&rft.isbn=978-0-19-957862-7&rft.aulast=Glynn&rft.aufirst=Ian&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">Helmholtz, Hermann von (1850).<i>Vorläufiger Bericht über die Fortpflanzungs-Geschwindigkeit der Nervenreizung</i>. In: Archiv für Anatomie, Physiologie und wissenschaftliche Medicin. Veit & Comp., pp. 71–73. <a rel="nofollow" class="external text" href="http://vlp.mpiwg-berlin.mpg.de/library/data/lit29168">MPIWG Berlin</a></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">Helmholtz, Hermann von (1850). <i>Messungen über den zeitlichen Verlauf der Zuckung animalischer Muskeln und die Fortpflanzungsgeschwindigkeit der Reizung in den Nerven</i>. In: Archiv für Anatomie, Physiologie und wissenschaftliche Medicin. Veit & Comp., pp. 276–364. <a rel="nofollow" class="external text" href="http://vlp.mpiwg-berlin.mpg.de/library/data/lit1862">MPIWG Berlin</a></span> </li> <li id="cite_note-Helmholtz1885-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-Helmholtz1885_13-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFvon_Helmholtz1885" class="citation book cs1">von Helmholtz, Hermann (1885). <a rel="nofollow" class="external text" href="https://archive.org/details/onsensationston00unkngoog"><i>On the sensations of tone as a physiological basis for the theory of music</i></a>. Translated by Ellis, Alexander J. (Second English ed.). London: Longmans, Green, and Co. p. <a rel="nofollow" class="external text" href="https://archive.org/details/onsensationston00unkngoog/page/n69">44</a><span class="reference-accessdate">. Retrieved <span class="nowrap">12 October</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=On+the+sensations+of+tone+as+a+physiological+basis+for+the+theory+of+music&rft.place=London&rft.pages=44&rft.edition=Second+English&rft.pub=Longmans%2C+Green%2C+and+Co.&rft.date=1885&rft.aulast=von+Helmholtz&rft.aufirst=Hermann&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fonsensationston00unkngoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.pbs.org/wgbh/amex/telephone/peopleevents/mabell.html">"PBS, American Experience: The Telephone – More About Bell"</a>. <i><a href="/wiki/PBS" title="PBS">PBS</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=PBS&rft.atitle=PBS%2C+American+Experience%3A+The+Telephone+%E2%80%93+More+About+Bell&rft_id=https%3A%2F%2Fwww.pbs.org%2Fwgbh%2Famex%2Ftelephone%2Fpeopleevents%2Fmabell.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-MacKenzie2008-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-MacKenzie2008_15-0">^</a></b></span> <span class="reference-text">MacKenzie 2003, p. 41.</span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text">Groundwater 2005, p. 31.</span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">Shulman 2008, pp. 46–48.</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHermann_L._F._Helmholtz,_M.D.1912" class="citation book cs1">Hermann L. F. Helmholtz, M.D. (1912). <a rel="nofollow" class="external text" href="https://archive.org/details/onsensationston01helmgoog"><i>On the Sensations of Tone as a Physiological Basis for the Theory of Music</i></a> (Fourth ed.). Longmans, Green, and Co. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781419178931" title="Special:BookSources/9781419178931"><bdi>9781419178931</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=On+the+Sensations+of+Tone+as+a+Physiological+Basis+for+the+Theory+of+Music&rft.edition=Fourth&rft.pub=Longmans%2C+Green%2C+and+Co&rft.date=1912&rft.isbn=9781419178931&rft.au=Hermann+L.+F.+Helmholtz%2C+M.D.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fonsensationston01helmgoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKoenigsberger2018" class="citation book cs1">Koenigsberger, Leo (28 March 2018). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=JCNWAAAAMAAJ&q=electrical+oscillation+helmholtz&pg=PA268"><i>Hermann von Helmholtz</i></a>. Clarendon press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-21517-4" title="Special:BookSources/978-0-486-21517-4"><bdi>978-0-486-21517-4</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">28 March</span> 2018</span> – via Google Books.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Hermann+von+Helmholtz&rft.pub=Clarendon+press&rft.date=2018-03-28&rft.isbn=978-0-486-21517-4&rft.aulast=Koenigsberger&rft.aufirst=Leo&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DJCNWAAAAMAAJ%26q%3Delectrical%2Boscillation%2Bhelmholtz%26pg%3DPA268&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text">John D. Jackson, Classical Electrodynamics, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-30932-X" title="Special:BookSources/0-471-30932-X">0-471-30932-X</a>.</span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHelmholtz1977" class="citation book cs1">Helmholtz, Hermann von (1977). <a rel="nofollow" class="external text" href="https://link.springer.com/content/pdf/10.1007/978-94-010-1115-0_1?pdf=chapter%20toc">"On the Origin and Significance of the Axioms of Geometry"</a>. <i>Epistemological Writings</i>. Boston Studies in the Philosophy of Science. Vol. 37. pp. <span class="nowrap">1–</span>38. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-94-010-1115-0_1">10.1007/978-94-010-1115-0_1</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-90-277-0582-2" title="Special:BookSources/978-90-277-0582-2"><bdi>978-90-277-0582-2</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">13 October</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=On+the+Origin+and+Significance+of+the+Axioms+of+Geometry&rft.btitle=Epistemological+Writings&rft.series=Boston+Studies+in+the+Philosophy+of+Science&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1-%3C%2Fspan%3E38&rft.date=1977&rft_id=info%3Adoi%2F10.1007%2F978-94-010-1115-0_1&rft.isbn=978-90-277-0582-2&rft.aulast=Helmholtz&rft.aufirst=Hermann+von&rft_id=https%3A%2F%2Flink.springer.com%2Fcontent%2Fpdf%2F10.1007%2F978-94-010-1115-0_1%3Fpdf%3Dchapter%2520toc&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDe_Kock2018" class="citation journal cs1">De Kock, Liesbet (2018). <a rel="nofollow" class="external text" href="https://jhaponline.org/jhap/article/view/3432">"Historicizing Hermann von Helmholtz's Psychology of Differentiation"</a>. <i>Journal for the History of Analytical Philosophy</i>. <b>6</b> (3). <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.15173%2Fjhap.v6i3.3432">10.15173/jhap.v6i3.3432</a></span>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/1854%2FLU-8552480">1854/LU-8552480</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:187618324">187618324</a><span class="reference-accessdate">. Retrieved <span class="nowrap">1 January</span> 2022</span>. <q>Hermann von Helmholtz's peculiar wavering between empiricism and transcendentalism in his philosophy of science in general, and in his theory of perception in particular, is a much debated and well-documented topic in the history and philosophy of science.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+for+the+History+of+Analytical+Philosophy&rft.atitle=Historicizing+Hermann+von+Helmholtz%27s+Psychology+of+Differentiation&rft.volume=6&rft.issue=3&rft.date=2018&rft_id=info%3Ahdl%2F1854%2FLU-8552480&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A187618324%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.15173%2Fjhap.v6i3.3432&rft.aulast=De+Kock&rft.aufirst=Liesbet&rft_id=https%3A%2F%2Fjhaponline.org%2Fjhap%2Farticle%2Fview%2F3432&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://search.amphilsoc.org/memhist/search?creator=&title=&subject=&subdiv=&mem=&year=1873&year-max=1873&dead=&keyword=&smode=advanced">"APS Member History"</a>. <i>search.amphilsoc.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">3 May</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=search.amphilsoc.org&rft.atitle=APS+Member+History&rft_id=https%3A%2F%2Fsearch.amphilsoc.org%2Fmemhist%2Fsearch%3Fcreator%3D%26title%3D%26subject%3D%26subdiv%3D%26mem%3D%26year%3D1873%26year-max%3D1873%26dead%3D%26keyword%3D%26smode%3Dadvanced&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20180203005705/http://www.igp-web.com/IGPArchives/ire/countrywide/xmisc/rcsi-hon-fellows.txt">"Honorary Fellows of the Royal College of Surgeons (RCSI) since 1784"</a>. Ireland Genealogy Project. 2013. Archived from <a rel="nofollow" class="external text" href="http://www.igp-web.com/IGPArchives/ire/countrywide/xmisc/rcsi-hon-fellows.txt">the original</a> on 3 February 2018<span class="reference-accessdate">. Retrieved <span class="nowrap">4 August</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Honorary+Fellows+of+the+Royal+College+of+Surgeons+%28RCSI%29+since+1784&rft.pub=Ireland+Genealogy+Project&rft.date=2013&rft_id=http%3A%2F%2Fwww.igp-web.com%2FIGPArchives%2Fire%2Fcountrywide%2Fxmisc%2Frcsi-hon-fellows.txt&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.iesis.org/honorary-fellows.html">"Honorary Members and Fellows"</a>. The Institution of Engineers and Shipbuilders in Scotland.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Honorary+Members+and+Fellows&rft.pub=The+Institution+of+Engineers+and+Shipbuilders+in+Scotland&rft_id=http%3A%2F%2Fwww.iesis.org%2Fhonorary-fellows.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-History-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-History_26-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20120414190640/http://www.helmholtz.de/en/about_us/history/">"History of the name in the About section of Helmholtz Association website"</a>. 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Retrieved <span class="nowrap">30 April</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=History+of+the+name+in+the+About+section+of+Helmholtz+Association+website&rft_id=http%3A%2F%2Fwww.helmholtz.de%2Fen%2Fabout_us%2Fhistory&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-Asteroid-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-Asteroid_27-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.minorplanetcenter.net/db_search/show_object?object_id=11573">"11573 Helmholtz (1993 SK3)"</a>. <i><a href="/wiki/Minor_Planet_Center" title="Minor Planet Center">Minor Planet Center</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">2 February</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Minor+Planet+Center&rft.atitle=11573+Helmholtz+%281993+SK3%29&rft_id=https%3A%2F%2Fwww.minorplanetcenter.net%2Fdb_search%2Fshow_object%3Fobject_id%3D11573&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation encyclopaedia cs1"><a rel="nofollow" class="external text" href="https://planetarynames.wr.usgs.gov/Feature/2438">"Lunar crater Helmholtz"</a>. <i>Gazetteer of Planetary Nomenclature</i>. USGS Astrogeology Research Program.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Lunar+crater+Helmholtz&rft.btitle=Gazetteer+of+Planetary+Nomenclature&rft.pub=USGS+Astrogeology+Research+Program&rft_id=https%3A%2F%2Fplanetarynames.wr.usgs.gov%2FFeature%2F2438&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation encyclopaedia cs1"><a rel="nofollow" class="external text" href="https://planetarynames.wr.usgs.gov/Feature/2439">"Martian crater Helmholtz"</a>. <i>Gazetteer of Planetary Nomenclature</i>. USGS Astrogeology Research Program.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Martian+crater+Helmholtz&rft.btitle=Gazetteer+of+Planetary+Nomenclature&rft.pub=USGS+Astrogeology+Research+Program&rft_id=https%3A%2F%2Fplanetarynames.wr.usgs.gov%2FFeature%2F2439&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.berlin.de/ba-charlottenburg-wilmersdorf/ueber-den-bezirk/freiflaechen/strassen/artikel.177427.php">"Helmholtzstraße"</a>. <i>berlin.de</i>. 21 September 2014<span class="reference-accessdate">. Retrieved <span class="nowrap">18 July</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=berlin.de&rft.atitle=Helmholtzstra%C3%9Fe&rft.date=2014-09-21&rft_id=https%3A%2F%2Fwww.berlin.de%2Fba-charlottenburg-wilmersdorf%2Fueber-den-bezirk%2Ffreiflaechen%2Fstrassen%2Fartikel.177427.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Sources">Sources</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=19" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Cahan, David <i>Helmholtz: A Life in Science.</i> University of Chicago Press, 2018. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-226-48114-2" title="Special:BookSources/978-0-226-48114-2">978-0-226-48114-2</a>.</li> <li>Cohen, Robert, and <a href="/wiki/Marx_W._Wartofsky" title="Marx W. Wartofsky">Wartofsky, Marx</a>, eds. and trans. Reidel. <i>Helmholtz: Epistemological Writings</i>, 1977.</li> <li>Ewald, William B., ed. <i>From Kant to Hilbert: A Source Book in the Foundations of Mathematics</i>, 2 vols. Oxford Uni. Press, 1996. <ul><li>1876. "The origin and meaning of geometrical axioms", 663–88.</li> <li>1878. "The facts in perception", 698–726.</li> <li>1887. "Numbering and measuring from an epistemological viewpoint", 727–52.</li></ul></li> <li>Groundwater, Jennifer. <i>Alexander Graham Bell: The Spirit of Invention</i>. Calgary: Altitude Publishing, 2005. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-55439-006-0" title="Special:BookSources/1-55439-006-0">1-55439-006-0</a>.</li> <li>Jackson, Myles W. <i>Harmonious Triads: Physicists, Musicians, and Instrument Makers in Nineteenth-Century Germany</i> (MIT Press, 2006).</li> <li>Kahl, Russell, ed. Wesleyan. <i>Selected Writings of Hermann von Helmholtz</i>, Uni. Press., 1971.</li> <li>Koenigsberger, Leo. <i>Hermann von Helmholtz</i>, translated by Frances A. Welby (Dover, 1965)</li> <li>MacKenzie, Catherine. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=iFOcw4lN_ZYC"><i>Alexander Graham Bell</i>.</a> Whitefish, Montana: Kessinger Publishing, 2003. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7661-4385-2" title="Special:BookSources/978-0-7661-4385-2">978-0-7661-4385-2</a>. Retrieved 29 July 2009.</li> <li>Shulman, Seth. <i><a href="/wiki/The_Telephone_Gambit" class="mw-redirect" title="The Telephone Gambit">The Telephone Gambit</a>: Chasing Alexander Bell's Secret</i>. New York: Norton & Company, 2008. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-393-06206-9" title="Special:BookSources/978-0-393-06206-9">978-0-393-06206-9</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=20" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcKendrick1899" class="citation book cs1">McKendrick, John Gray (1899). <a rel="nofollow" class="external text" href="https://archive.org/details/hermannludwig00mckeiala/"><i>Hermann Ludwig Ferdinand von Helmholtz</i></a>. T. Fisher Unwin.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Hermann+Ludwig+Ferdinand+von+Helmholtz&rft.pub=T.+Fisher+Unwin&rft.date=1899&rft.aulast=McKendrick&rft.aufirst=John+Gray&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhermannludwig00mckeiala%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKoenigsberger1906" class="citation book cs1">Koenigsberger, Leo (1906). <a rel="nofollow" class="external text" href="https://archive.org/details/hermannvonhelmho00koenrich/hermannvonhelmho00koenrich/"><i>Hermann von Helmholtz</i></a>. Oxford Clarendon Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Hermann+von+Helmholtz&rft.pub=Oxford+Clarendon+Press&rft.date=1906&rft.aulast=Koenigsberger&rft.aufirst=Leo&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhermannvonhelmho00koenrich%2Fhermannvonhelmho00koenrich%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></li> <li>David Cahan: <i>Helmholtz: A Life in Science</i> (University of Chicago, 2018). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-226-48114-2" title="Special:BookSources/978-0-226-48114-2">978-0-226-48114-2</a> <ul><li><a href="/wiki/Steven_Shapin" title="Steven Shapin">Steven Shapin</a>, "A Theorist of (Not Quite) Everything" (review of David Cahan, <i>Helmholtz: A Life in Science</i>, University of Chicago Press, 2018, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-226-48114-2" title="Special:BookSources/978-0-226-48114-2">978-0-226-48114-2</a>, 937 pp.), <i><a href="/wiki/The_New_York_Review_of_Books" title="The New York Review of Books">The New York Review of Books</a></i>, vol. 66, no. 15 (10 October 2019), pp. 29–31.</li></ul></li></ul> <ul><li>David Cahan (Ed.): <i>Hermann von Helmholtz and the Foundations of Nineteenth-Century Science.</i> Univ. California, Berkeley 1994, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-520-08334-9" title="Special:BookSources/978-0-520-08334-9">978-0-520-08334-9</a>.</li> <li>Gregor Schiemann: <i>Hermann von Helmholtz's Mechanism: The Loss of Certainty. A Study on the Transition from Classical to Modern Philosophy of Nature</i>. Dordrecht: Springer 2009, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4020-5629-1" title="Special:BookSources/978-1-4020-5629-1">978-1-4020-5629-1</a>.</li></ul> <ul><li>Franz Werner: <i>Hermann Helmholtz´ Heidelberger Jahre (1858–1871)</i>. (= Sonderveröffentlichungen des Stadtarchivs Heidelberg 8). Mit 52 Abbildungen. Berlin / Heidelberg (Springer) 1997.</li> <li>Kenneth L. Caneva: <i><a rel="nofollow" class="external text" href="https://mitpress.mit.edu/9780262045735/helmholtz-and-the-conservation-of-energy/">Helmholtz and the Conservation of Energy: Contexts of Creation and Reception</a></i>. The MIT Press, Cambridge, MA, 2021, ISBN 978-0-262-04573-5</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_von_Helmholtz&action=edit&section=21" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output 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data-file-height="1376" /></a></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Hermann_von_Helmholtz" class="extiw" title="commons:Category:Hermann von Helmholtz">Hermann von Helmholtz</a></span>.</div></div> </div> <ul><li>"<a rel="nofollow" class="external text" href="https://books.google.com.hk/books?id=5aUOAAAAIAAJ&pg=PR17">Hermann von Helmholtz</a>" (Obituary). Royal Society (Great Britain). (1894). <i>Proceedings of the Royal Society of London</i>. London: Printed by Taylor and Francis. p. xvii.</li> <li>"<a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/hermann-helmholtz">Hermann von Helmholtz</a>" in <a href="/wiki/Stanford_Encyclopedia_of_Philosophy" title="Stanford Encyclopedia of Philosophy">Stanford Encyclopedia of Philosophy</a>, written by Lydia Patton</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://ancestors.familysearch.org/en/MG9M-XWN">"Prof. Dr. Hermann Ludwig Ferdinand von Helmholtz"</a>, <i><a href="/wiki/FamilySearch" title="FamilySearch">FamilySearch</a></i></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Prof.+Dr.+Hermann+Ludwig+Ferdinand+von+Helmholtz&rft.btitle=FamilySearch&rft_id=https%3A%2F%2Fancestors.familysearch.org%2Fen%2FMG9M-XWN&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'ConnorRobertson" class="citation cs2">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" class="mw-redirect" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Helmholtz.html">"Hermann von Helmholtz"</a>, <i><a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a></i>, <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Hermann+von+Helmholtz&rft.btitle=MacTutor+History+of+Mathematics+Archive&rft.pub=University+of+St+Andrews&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FBiographies%2FHelmholtz.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+von+Helmholtz" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://vlp.mpiwg-berlin.mpg.de/people/data?id=per87">Biography, bibliography and access to digital sources</a> in the <a href="/wiki/Virtual_Laboratory" title="Virtual Laboratory">Virtual Laboratory</a> of the <a href="/wiki/Max_Planck_Institute_for_the_History_of_Science" title="Max Planck Institute for the History of Science">Max Planck Institute for the History of Science</a></li> <li><a href="https://imslp.org/wiki/Category:Helmholtz,_Hermann_von" class="extiw" title="scores:Category:Helmholtz, Hermann von">Free scores by Hermann von Helmholtz</a> at the <a href="/wiki/International_Music_Score_Library_Project" title="International Music Score Library Project">International Music Score Library Project</a> (IMSLP) (<i>Die Lehre von den Tonempfindungen</i>)</li> <li>Helmholtz's (1867) <a rel="nofollow" class="external text" href="http://lhldigital.lindahall.org/cdm/ref/collection/color/id/10550"><i>Handbuch der physiologischen Optik</i></a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190412080803/http://lhldigital.lindahall.org/cdm/ref/collection/color/id/10550">Archived</a> 12 April 2019 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> – digital facsimile from the <a href="/wiki/Linda_Hall_Library" title="Linda Hall Library">Linda Hall Library</a></li> <li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=49057">Hermann von Helmholtz</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></li> <li><a rel="nofollow" class="external text" href="https://librivox.org/author/16353">Works by Hermann von Helmholtz</a> at <a href="/wiki/LibriVox" title="LibriVox">LibriVox</a> (public domain audiobooks) <span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Speaker_Icon.svg/15px-Speaker_Icon.svg.png" decoding="async" width="15" height="15" 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.navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Copley_Medallists_(1851–1900)35" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Copley_Medallists_1851%E2%80%931900" title="Template:Copley Medallists 1851–1900"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Copley_Medallists_1851%E2%80%931900" title="Template talk:Copley Medallists 1851–1900"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Copley_Medallists_1851%E2%80%931900" title="Special:EditPage/Template:Copley Medallists 1851–1900"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Copley_Medallists_(1851–1900)35" style="font-size:114%;margin:0 4em"><a href="/wiki/Copley_Medal" title="Copley Medal">Copley Medallists</a> (1851–1900)</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Richard_Owen" title="Richard Owen">Richard Owen</a> (1851)</span></li> <li><span class="nowrap"><a href="/wiki/Alexander_von_Humboldt" title="Alexander von Humboldt">Alexander von Humboldt</a> (1852)</span></li> <li><span class="nowrap"><a href="/wiki/Heinrich_Wilhelm_Dove" title="Heinrich Wilhelm Dove">Heinrich Wilhelm Dove</a> (1853)</span></li> <li><span class="nowrap"><a href="/wiki/Johannes_Peter_M%C3%BCller" title="Johannes Peter Müller">Johannes Peter Müller</a> (1854)</span></li> <li><span class="nowrap"><a href="/wiki/L%C3%A9on_Foucault" title="Léon Foucault">Léon Foucault</a> (1855)</span></li> <li><span class="nowrap"><a href="/wiki/Henri_Milne-Edwards" title="Henri Milne-Edwards">Henri Milne-Edwards</a> (1856)</span></li> <li><span class="nowrap"><a href="/wiki/Michel_Eug%C3%A8ne_Chevreul" title="Michel Eugène Chevreul">Michel Eugène Chevreul</a> (1857)</span></li> <li><span class="nowrap"><a href="/wiki/Charles_Lyell" title="Charles Lyell">Charles Lyell</a> (1858)</span></li> <li><span class="nowrap"><a href="/wiki/Wilhelm_Eduard_Weber" title="Wilhelm Eduard Weber">Wilhelm Eduard Weber</a> (1859)</span></li> <li><span class="nowrap"><a href="/wiki/Robert_Bunsen" title="Robert Bunsen">Robert Bunsen</a> (1860)</span></li> <li><span class="nowrap"><a href="/wiki/Louis_Agassiz" title="Louis Agassiz">Louis Agassiz</a> (1861)</span></li> <li><span class="nowrap"><a href="/wiki/Thomas_Graham_(chemist)" title="Thomas Graham (chemist)">Thomas Graham</a> (1862)</span></li> <li><span class="nowrap"><a href="/wiki/Adam_Sedgwick" title="Adam Sedgwick">Adam Sedgwick</a> (1863)</span></li> <li><span class="nowrap"><a href="/wiki/Charles_Darwin" title="Charles Darwin">Charles Darwin</a> (1864)</span></li> <li><span class="nowrap"><a href="/wiki/Michel_Chasles" title="Michel Chasles">Michel Chasles</a> (1865)</span></li> <li><span class="nowrap"><a href="/wiki/Julius_Pl%C3%BCcker" title="Julius Plücker">Julius Plücker</a> (1866)</span></li> <li><span class="nowrap"><a href="/wiki/Karl_Ernst_von_Baer" title="Karl Ernst von Baer">Karl Ernst von Baer</a> (1867)</span></li> <li><span class="nowrap"><a href="/wiki/Charles_Wheatstone" title="Charles Wheatstone">Charles Wheatstone</a> (1868)</span></li> <li><span class="nowrap"><a href="/wiki/Henri_Victor_Regnault" title="Henri Victor Regnault">Henri Victor Regnault</a> (1869)</span></li> <li><span class="nowrap"><a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">James Prescott Joule</a> (1870)</span></li> <li><span class="nowrap"><a href="/wiki/Julius_von_Mayer" title="Julius von Mayer">Julius Robert von Mayer</a> (1871)</span></li> <li><span class="nowrap"><a href="/wiki/Friedrich_W%C3%B6hler" title="Friedrich Wöhler">Friedrich Wöhler</a> (1872)</span></li> <li><span class="nowrap"><a class="mw-selflink selflink">Hermann von Helmholtz</a> (1873)</span></li> <li><span class="nowrap"><a href="/wiki/Louis_Pasteur" title="Louis Pasteur">Louis Pasteur</a> (1874)</span></li> <li><span class="nowrap"><a href="/wiki/August_Wilhelm_von_Hofmann" title="August Wilhelm von Hofmann">August Wilhelm von Hofmann</a> (1875)</span></li> <li><span class="nowrap"><a href="/wiki/Claude_Bernard" title="Claude Bernard">Claude Bernard</a> (1876)</span></li> <li><span class="nowrap"><a href="/wiki/James_Dwight_Dana" title="James Dwight Dana">James Dwight Dana</a> (1877)</span></li> <li><span class="nowrap"><a href="/wiki/Jean-Baptiste_Boussingault" title="Jean-Baptiste Boussingault">Jean-Baptiste Boussingault</a> (1878)</span></li> <li><span class="nowrap"><a href="/wiki/Rudolf_Clausius" title="Rudolf Clausius">Rudolf Clausius</a> (1879)</span></li> <li><span class="nowrap"><a href="/wiki/James_Joseph_Sylvester" title="James Joseph Sylvester">James Joseph Sylvester</a> (1880)</span></li> <li><span class="nowrap"><a href="/wiki/Charles_Adolphe_Wurtz" title="Charles Adolphe Wurtz">Charles Adolphe Wurtz</a> (1881)</span></li> <li><span class="nowrap"><a href="/wiki/Arthur_Cayley" title="Arthur Cayley">Arthur Cayley</a> (1882)</span></li> <li><span class="nowrap"><a href="/wiki/Lord_Kelvin" title="Lord Kelvin">William Thomson</a> (1883)</span></li> <li><span class="nowrap"><a href="/wiki/Carl_Ludwig" title="Carl Ludwig">Carl Ludwig</a> (1884)</span></li> <li><span class="nowrap"><a href="/wiki/August_Kekul%C3%A9" title="August Kekulé">Friedrich August Kekulé von Stradonitz</a> (1885)</span></li> <li><span class="nowrap"><a href="/wiki/Franz_Ernst_Neumann" title="Franz Ernst Neumann">Franz Ernst Neumann</a> (1886)</span></li> <li><span class="nowrap"><a href="/wiki/Joseph_Dalton_Hooker" title="Joseph Dalton Hooker">Joseph Dalton Hooker</a> (1887)</span></li> <li><span class="nowrap"><a href="/wiki/Thomas_Henry_Huxley" title="Thomas Henry Huxley">Thomas Henry Huxley</a> (1888)</span></li> <li><span class="nowrap"><a href="/wiki/George_Salmon" title="George Salmon">George Salmon</a> (1889)</span></li> <li><span class="nowrap"><a href="/wiki/Simon_Newcomb" title="Simon Newcomb">Simon Newcomb</a> (1890)</span></li> <li><span class="nowrap"><a href="/wiki/Stanislao_Cannizzaro" title="Stanislao Cannizzaro">Stanislao Cannizzaro</a> (1891)</span></li> <li><span class="nowrap"><a href="/wiki/Rudolf_Virchow" title="Rudolf Virchow">Rudolf Virchow</a> (1892)</span></li> <li><span class="nowrap"><a href="/wiki/Sir_George_Stokes,_1st_Baronet" title="Sir George Stokes, 1st Baronet">George Gabriel Stokes</a> (1893)</span></li> <li><span class="nowrap"><a href="/wiki/Edward_Frankland" title="Edward Frankland">Edward Frankland</a> (1894)</span></li> <li><span class="nowrap"><a href="/wiki/Karl_Weierstrass" title="Karl Weierstrass">Karl Weierstrass</a> (1895)</span></li> <li><span class="nowrap"><a href="/wiki/Carl_Gegenbaur" title="Carl Gegenbaur">Carl Gegenbaur</a> (1896)</span></li> <li><span class="nowrap"><a href="/wiki/Albert_von_K%C3%B6lliker" title="Albert von Kölliker">Albert von Kölliker</a> (1897)</span></li> <li><span class="nowrap"><a href="/wiki/William_Huggins" title="William Huggins">William Huggins</a> (1898)</span></li> <li><span class="nowrap"><a href="/wiki/John_William_Strutt,_3rd_Baron_Rayleigh" title="John William Strutt, 3rd Baron Rayleigh">John William Strutt</a> (1899)</span></li> <li><span class="nowrap"><a href="/wiki/Marcellin_Berthelot" title="Marcellin Berthelot">Marcellin Berthelot</a> (1900)</span></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1038841319"><link rel="mw-deduplicated-inline-style" 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href="https://isni.org/isni/0000000121326382">ISNI</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/51690801">VIAF</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.worldcat.org/fast/43375/">FAST</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Hermann von Helmholtz"><a rel="nofollow" class="external text" href="https://id.oclc.org/worldcat/entity/E39PBJwX8rQwGmkhjM48kvHHmd">WorldCat</a></span></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Helmholtz, Hermann von"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/11854893X">Germany</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/n79112262">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb119071971">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb119071971">BnF data</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00518409">Japan</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://nla.gov.au/anbd.aut-an35186200">Australia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=jn20000720103&CON_LNG=ENG">Czech Republic</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX1302973">Spain</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.bnportugal.gov.pt/aut/catbnp/240166">Portugal</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://data.bibliotheken.nl/id/thes/p070546452">Netherlands</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://authority.bibsys.no/authority/rest/authorities/html/90273718">Norway</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://kopkatalogs.lv/F?func=direct&local_base=lnc10&doc_number=000072519&P_CON_LNG=ENG">Latvia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://katalog.nsk.hr/F/?func=direct&doc_number=000289175&local_base=nsk10">Croatia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://www.bncatalogo.cl/F?func=direct&local_base=red10&doc_number=000196808">Chile</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.nlg.gr/cgi-bin/koha/opac-authoritiesdetail.pl?authid=158309">Greece</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://lod.nl.go.kr/resource/KAC2018F7760">Korea</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://libris.kb.se/86lnr28s2htm865">Sweden</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dbn.bn.org.pl/descriptor-details/9811565560605606">Poland</a></span><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://dbn.bn.org.pl/descriptor-details/9810653942505606">2</a></span></li></ul></li><li><span class="uid"><a class="external text" href="https://wikidata-externalid-url.toolforge.org/?p=8034&url_prefix=https://opac.vatlib.it/auth/detail/&id=495/76308">Vatican</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007262423505171">Israel</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://cantic.bnc.cat/registre/981058514345606706">Catalonia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://opac.kbr.be/LIBRARY/doc/AUTHORITY/14079237">Belgium</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Academics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/author/DA01295293?l=en">CiNii</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.mathgenealogy.org/id.php?id=49057">Mathematics Genealogy Project</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.scopus.com/authid/detail.uri?authorId=56907714800">Scopus</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:von-helmholtz.hermann">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dblp.org/pid/203/3848">DBLP</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/84020">MathSciNet</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Artists</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://pic.nypl.org/constituents/186319">Photographers' Identities</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://trove.nla.gov.au/people/856589">Trove</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Helmholtz, Hermann Ludwig Ferdinand von (preußischer Adel 1883)"><a rel="nofollow" class="external text" href="https://www.deutsche-biographie.de/11854893X.html?language=en">Deutsche Biographie</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-digitale-bibliothek.de/person/gnd/11854893X">DDB</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/031053130">IdRef</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://snaccooperative.org/ark:/99166/w6qf9187">SNAC</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Hermann_von_Helmholtz&oldid=1267312503">https://en.wikipedia.org/w/index.php?title=Hermann_von_Helmholtz&oldid=1267312503</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" 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