Editing Carl Friedrich Gauss (section)

=== Magnetism and telegraphy ===
==== Geomagnetism ====
[[File:Göttingen-Gauß-Weber-Monument.01.JPG|thumb|upright|Gauss-Weber monument in Göttingen by Ferdinand Hartzer (1899)]]
[[File:A magnetometer used by Carl Friedrich Gauss, from Gerlach und F. Traumüller, 1899.png|thumb|The Gauss–Weber magnetometer]]
Gauss had been interested in magnetism since 1803.{{sfn|Dunnington|2004|p=153}} After [[Alexander von Humboldt]] visited Göttingen in 1826, both scientists began intensive research on [[geomagnetism]], partly independently, partly in productive cooperation.<ref>{{cite journal | author-last = Reich | author-first = Karin  | title = Alexander von Humboldt und Carl Friedrich Gauss als Wegbereiter der neuen Disziplin Erdmagnetismus | journal = Humboldt Im Netz | volume = 12 | issue = 22 | pages = 33–55 | year = 2011 | language = de | url = https://www.hin-online.de/index.php/hin/article/view/154/280}}</ref> In 1828, Gauss was Humboldt's guest during the conference of the [[Society of German Natural Scientists and Physicians]] in Berlin, where he got acquainted with the physicist [[Wilhelm Eduard Weber|Wilhelm Weber]].{{sfn|Dunnington|2004|p=136}}

When Weber got the chair for physics in Göttingen as successor of [[Johann Tobias Mayer]] by Gauss's recommendation in 1831, both of them started a fruitful collaboration, leading to a new knowledge of [[magnetism]] with a representation for the unit of magnetism in terms of mass, charge, and time.{{sfn|Dunnington|2004|p=161}} They founded the ''Magnetic Association'' (German: ''Magnetischer Verein''), an international working group of several observatories, which carried out measurements of [[Earth's magnetic field]] in many regions of the world using equivalent methods at arranged dates in the years 1836 to 1841.<ref name="Reich">{{cite journal | author-last = Reich | author-first = Karin  | title = Der Humboldt'sche Magnetische Verein im historischen Kontext | journal = Humboldt Im Netz | volume = 24 | issue = 46 | pages = 53–74 | year = 2023 | language = de | url = https://www.hin-online.de/index.php/hin/article/view/357/719}}</ref>

In 1836, Humboldt suggested the establishment of a worldwide net of geomagnetic stations in the [[British Empire|British dominions]] with a letter to the [[Prince Augustus Frederick, Duke of Sussex|Duke of Sussex]], then president of the Royal Society; he proposed that magnetic measures should be taken under standardized conditions using his methods.<ref>{{cite journal | author-last = Biermann | author-first = Kurt-R. | title = Aus der Vorgeschichte der Aufforderung Alexander von Humboldt von 1836 an den Präsidenten der Royal Society zur Errichtung geomagnetischer Stationen (Dokumente zu den Beziehungen zwischen A.v. Humboldt und C. F. Gauß) | journal = Humboldt Im Netz | volume = 6 | issue = 11 | year = 2005 | language = de | url = https://www.hin-online.de/index.php/hin/article/view/154/280}}</ref><ref>{{cite journal | author-last = Humboldt | author-first = Alexander von | title = Letter of the Baron von Humboldt to His Royal Highness the Duke of Sussex,..., on the Advancement of the Knowledge of Terrestrial Magnetism, by the Establishment of Magnetic Stations and correspionding Observations | journal = [[Philosophical Magazine]] | issue = 9 | pages = 42–53 | year = 1836 | volume = Bd. 6 | doi = 10.18443/70 | url = https://www.hin-online.de/index.php/hin/article/view/70/112}}</ref> Together with other instigators, this led to a global program known as "[[Edward Sabine#Magnetical crusade|Magnetical crusade]]" under the direction of [[Edward Sabine]]. The dates, times, and intervals of observations were determined in advance, the ''Göttingen mean time'' was used as the standard.<ref name="Rupke">{{cite book | last1 = Rupke | first1 = Nicolaas | author-link  = Nicolaas Adrianus Rupke | editor-last = Mittler | editor-first = Elmar | title = "Wie der Blitz einschlägt, hat sich das Räthsel gelöst" – Carl Friedrich Gauß in Göttingen | publisher = Niedersächsische Staats- und Universitätsbibliothek | date = 2005 | series = Göttinger Bibliotheksschriften 30 | pages = 188–201 | chapter = Carl Friedrich Gauß und der Erdmagnetismus | isbn = 3-930457-72-5 | language = de | url = http://webdoc.sub.gwdg.de/ebook/e/2005/gausscd/html/Katalog.pdf}}</ref> 61 stations on all five continents participated in this global program. Gauss and Weber founded a series for publication of the results, six volumes were edited between 1837 and 1843. Weber's departure to [[Leipzig University|Leipzig]] in 1843 as late effect of the [[Göttingen Seven|Göttingen Seven affair]] marked the end of Magnetic Association activity.<ref name="Reich" />

Following Humboldt's example, Gauss ordered a magnetic [[observatory]] to be built in the garden of the observatory, but the scientists differed over instrumental equipment; Gauss preferred stationary instruments, which he thought to give more precise results, whereas Humboldt was accustomed to movable instruments. Gauss was interested in the temporal and spatial variation of magnetic [[Magnetic declination|declination]], [[Magnetic dip|inclination]], and intensity and differentiated, unlike Humboldt, between "horizontal" and "vertical" intensity. Together with Weber, he developed methods of measuring the components of the intensity of the magnetic field and constructed a suitable [[magnetometer]] to measure ''absolute values'' of the strength of the Earth's magnetic field, not more relative ones that depended on the apparatus.<ref name="Reich" />{{sfn|Schaaf|1964|pp=115–127}} The precision of the magnetometer was about ten times higher than that of previous instruments. With this work, Gauss was the first to derive a non-mechanical quantity by basic mechanical quantities.<ref name="Rupke" />

Gauss carried out a ''General Theory of Terrestrial Magnetism'' (1839), in what he believed to describe the nature of magnetic force; according to Felix Klein, this work is a presentation of observations by use of [[spherical harmonics]] rather than a physical theory.{{sfn|Klein|1979|pp=21–23}} The theory predicted the existence of exactly two [[Poles of astronomical bodies#Magnetic poles|magnetic poles]] on the Earth, thus [[Christopher Hansteen|Hansteen]]'s idea of four magnetic poles became obsolete,<ref name="Roussanova">{{cite journal | author-last = Roussanova | author-first = Elena  | title = Russland ist seit jeher das gelobte Land für Magnetismus gewesen: Alexander von Humboldt, Carl Friedrich Gauß und die Erforschjung des Erdmagnetismus in Russland | journal = Humboldt Im Netz | volume = 12 | issue = 22 | pages = 56–83 | year = 2011 | language = de | url = https://www.hin-online.de/index.php/hin/article/view/155/282}}</ref> and the data allowed to determine their location with rather good precision.{{sfn|Schaefer|1929|p=87}}

Gauss influenced the beginning of geophysics in Russia, when [[Adolph Theodor Kupffer]], one of his former students, founded a magnetic observatory in [[St. Petersburg]], following the example of the observatory in Göttingen, and similarly, [[Ivan Simonov]] in [[Kazan]].<ref name="Roussanova"/>

==== Electromagnetism ====
[[File:Gauss-Weber-Telegraf Paulinerkirche 02.jpg|thumb|upright|Town plan of Göttingen with course of the telegraphic connection]]
The discoveries of [[Hans Christian Ørsted]] on [[electromagnetism]] and [[Michael Faraday]] on [[electromagnetic induction]] drew Gauss's attention to these matters.{{sfn|Schaefer|1929|p=6}} Gauss and Weber found rules for branched [[Electricity|electric]] circuits, which were later found independently and first published by [[Gustav Kirchhoff]] and named after him as [[Kirchhoff's circuit laws]],{{sfn|Schaefer|1929|p=108}} and made inquiries into electromagnetism. They constructed the first [[Electrical telegraph|electromechanical telegraph]] in 1833, and Weber himself connected the observatory with the institute for physics in the town centre of Göttingen,{{efn|A thunderstorm damaged the cable in 1845.<ref name="Timm" />}} but they made no further commercial use of this invention.<ref name="Timm">{{cite book | last1 = Timm | first1 = Arnulf | editor-last = Mittler | editor-first = Elmar | title = "Wie der Blitz einschlägt, hat sich das Räthsel gelöst" – Carl Friedrich Gauß in Göttingen | publisher = Niedersächsische Staats- und Universitätsbibliothek | date = 2005 | series = Göttinger Bibliotheksschriften 30 | pages = 169–183 | chapter = Der elektrische Telegraph von Gauß und Weber | language = de | isbn = 3-930457-72-5 | url = http://webdoc.sub.gwdg.de/ebook/e/2005/gausscd/html/Katalog.pdf}}</ref><ref>{{Cite book | last1 = Martín-Rodríguez | first1 = Fernando | last2  = Barrio García | first2 = Gonzalo | last3 = Álvarez Lires | first3 = María | title = 2010 Second Region 8 IEEE Conference on the History of Communications | chapter = Technological archaeology: Technical description of the Gauss-Weber telegraph | date = 2010 | chapter-url = https://ieeexplore.ieee.org/document/5735309 | pages = 1–4 | doi = 10.1109/HISTELCON.2010.5735309|hdl=11093/1859 | isbn = 978-1-4244-7450-9 | s2cid = 2359293}}</ref>

Gauss's main theoretical interests in electromagnetism were reflected in his attempts to formulate quantitive laws governing electromagnetic induction. In notebooks from these years, he recorded several innovative formulations; he discovered the [[vector potential]] function, independently rediscovered by [[Franz Ernst Neumann]] in 1845, and in January 1835 he wrote down an "induction law" equivalent to [[Faraday's law of induction|Faraday's law]], which stated that the [[electromotive force]] at a given point in space is equal to the [[instantaneous rate of change]] (with respect to time) of this function.<ref>Printed in the ''Collected Works'', Volume 5, pp. 609–610.</ref><ref>{{cite book | last = Roche | first = John J. | chapter = A critical study of the vector potential | editor-last = Roche | editor-first = John | date = 1990 | title = Physicists Look Back: Studies in the History of Physics | publisher = Adam Hilger | place = Bristol, New York | pages = 147–149 | isbn = 0-85274-001-8}}</ref>

Gauss tried to find a unifying law for long-distance effects of [[electrostatics]], [[electrodynamics]], electromagnetism, and [[electric Induction|induction]], comparable to Newton's law of gravitation,{{sfn|Schaefer|1929|pp=148–152}} but his attempt ended in a "tragic failure".<ref name="Rupke" />