Editing Tide (section)

=== History of tidal theory ===
{{further|Theory of tides#History}}

Investigation into tidal physics was important in the early development of [[celestial mechanics]], with the existence of two daily tides being explained by the Moon's gravity. Later the daily tides were explained more precisely by the interaction of the Moon's and the Sun's gravity.

[[Seleucus of Seleucia]] theorized around 150 BC that tides were caused by the Moon. The influence of the Moon on bodies of water was also mentioned in [[Ptolemy]]'s ''[[Tetrabiblos]]''.{{efn|"The moon, too, as the heavenly body nearest the earth, bestows her effluence most abundantly upon mundane things, for most of them, animate or inanimate, are sympathetic to her and change in company with her; the rivers increase and diminish their streams with her light, the seas turn their own tides with her rising and setting, ... "<ref>{{Cite book |author=[[Ptolemy]] |translator-first=Frank E. |translator-last=Robbins |title=Tetrabiblos |location=Cambridge, Massachusetts |publisher=[[Harvard University Press]] |date=1940 |volume=1 |chapter=2}}</ref>}}

In {{lang|la|De temporum ratione}} (''[[The Reckoning of Time]]'') of 725 [[Bede]] linked semidurnal tides and the phenomenon of varying tidal heights to the Moon and its phases. Bede starts by noting that the tides rise and fall 4/5 of an hour later each day, just as the Moon rises and sets 4/5 of an hour later.<ref name=Wallis>{{cite book |author=Bede |author-link=Bede |translator-last=Wallis |translator-first=Faith |title=The Reckoning of Time |year=1999 |publisher=[[Liverpool University Press]] |isbn=0-85323-693-3 |url=https://books.google.com/books?id=yFsw-Vaup6sC |access-date=1 June 2018 |page=82 |via=[[Google Books]] |archive-date=9 April 2023 |archive-url=https://web.archive.org/web/20230409160418/https://books.google.com/books?id=yFsw-Vaup6sC |url-status=live }}</ref> He goes on to emphasise that in two lunar months (59 days) the Moon circles the Earth 57 times and there are 114 tides.{{sfn|Bede|1999|p=83}} Bede then observes that the height of tides varies over the month. Increasing tides are called ''malinae'' and decreasing tides ''ledones'' and that the month is divided into four parts of seven or eight days with alternating ''malinae'' and ''ledones''.{{sfn|Bede|1999|p=84}} In the same passage he also notes the effect of winds to hold back tides.{{sfn|Bede|1999|p=84}} Bede also records that the time of tides varies from place to place. To the north of Bede's location ([[Monkwearmouth]]) the tides are earlier, to the south later.{{sfn|Bede|1999|p=85}} He explains that the tide "deserts these shores in order to be able all the more to be able to flood other [shores] when it arrives there" noting that "the Moon which signals the rise of tide here, signals its retreat in other regions far from this quarter of the heavens".{{sfn|Bede|1999|p=85}}

Later medieval understanding of the tides was primarily based on works of [[Muslim astronomers]], which became available through [[Latin translations of the 12th century|Latin translation]] starting from the 12th century.<ref name="Tolmacheva">{{Cite book |last=Tolmacheva |first=Marina |title=Medieval Science, Technology, and Medicine: An Encyclopedia: Geography, Chorography |work= |publisher=[[Routledge]] |year=2014 |isbn=978-1135459321 |editor1-last=Glick |editor1-first=Thomas F. |page=188}}</ref> [[Abu Ma'shar al-Balkhi]] (d. circa 886), in his {{lang|la|Introductorium in astronomiam}}, taught that ebb and flood tides were caused by the Moon.<ref name=Tolmacheva /> Abu Ma'shar discussed the effects of wind and Moon's phases relative to the Sun on the tides.<ref name=Tolmacheva /> In the 12th century, [[al-Bitruji]] (d. circa 1204) contributed the notion that the tides were caused by the general circulation of the heavens.<ref name=Tolmacheva />

[[Simon Stevin]], in his 1608 {{lang|nl|De spiegheling der Ebbenvloet}} (''The theory of ebb and flood''), dismissed a large number of misconceptions that still existed about ebb and flood. Stevin pleaded for the idea that the attraction of the Moon was responsible for the tides and spoke in clear terms about ebb, flood, [[spring tide]] and [[neap tide]], stressing that further research needed to be made.<ref>{{cite web |url=http://www.vliz.be/imisdocs/publications/224466.pdf |title=Simon Stevin |publisher=Flanders Marine Institute |type=pdf |language=nl |access-date=2014-06-01 |archive-date=2014-08-05 |archive-url=https://web.archive.org/web/20140805054735/http://www.vliz.be/imisdocs/publications/224466.pdf |url-status=live }}</ref><ref>{{Cite book |last1=Palmerino |first1=Carla Rita |first2=J.M.M.H. |last2=Thijssen |url=https://books.google.com/books?id=a5lkdlMPi1AC&dq=%22johannes+kepler%22+%22simon+stevin%22+ebb&pg=PA200 |title=The Reception of the Galilean Science of Motion in Seventeenth-Century Europe |date=31 August 2004 |publisher=[[Springer Science+Business Media]] |isbn=978-1-4020-2455-9 |page=200 |via=[[Google Books]] |access-date=29 November 2022 |archive-date=12 April 2022 |archive-url=https://web.archive.org/web/20220412060701/https://books.google.com/books?id=a5lkdlMPi1AC&pg=PA200&dq=%22johannes+kepler%22+%22simon+stevin%22+ebb |url-status=live }}</ref>

In 1609 [[Johannes Kepler]] also correctly suggested that the gravitation of the Moon caused the tides,{{efn|''"Orbis virtutis tractoriæ, quæ est in Luna, porrigitur utque ad Terras, & prolectat aquas sub Zonam Torridam, ... Celeriter vero Luna verticem transvolante, cum aquæ tam celeriter sequi non possint, fluxus quidem fit Oceani sub Torrida in Occidentem, ... "'' (The sphere of the lifting power, which is [centered] in the moon, is extended as far as to the earth and attracts the waters under the torrid zone, ... However the moon flies swiftly across the zenith; because the waters cannot follow so quickly, the tide of the ocean under the torrid [zone] is indeed made to the west, ..."<ref>Johannes Kepler, ''Astronomia nova'' ... (1609), p. 5 of the ''Introductio in hoc opus'' (Introduction to this work). [https://archive.org/stream/Astronomianovaa00Kepl#page/n24/mode/1up From page 5:]</ref>}} which he based upon ancient observations and correlations.

[[Galileo Galilei]] in his 1632 ''[[Dialogue Concerning the Two Chief World Systems]]'', whose working title was ''Dialogue on the Tides'', gave an explanation of the tides. The resulting theory, however, was incorrect as he attributed the tides to the sloshing of water caused by the Earth's movement around the Sun. He hoped to provide mechanical proof of the Earth's movement. The value of his tidal theory is disputed. Galileo rejected Kepler's explanation of the tides.

[[Isaac Newton]] (1642–1727) was the first person to explain tides as the product of the gravitational attraction of astronomical masses. His explanation of the tides (and many other phenomena) was published in the ''[[Philosophiae Naturalis Principia Mathematica|Principia]]'' (1687)<ref name=slc-ch2>{{cite book |author-link=Eugenie Lisitzin |last=Lisitzin |first=E. |title=Sea-Level Changes, (Elsevier Oceanography Series) |volume=8 |date=1974 |chapter=2 "Periodical sea-level changes: Astronomical tides" |page=5}}</ref><ref>{{cite web |publisher=U.S. [[National Oceanic and Atmospheric Administration]] (NOAA) National Ocean Service (Education section) |url=http://oceanservice.noaa.gov/education/kits/tides/tides02_cause.html |title=What Causes Tides? |access-date=2009-09-06 |archive-date=2016-08-20 |archive-url=https://web.archive.org/web/20160820055655/http://oceanservice.noaa.gov/education/kits/tides/tides02_cause.html |url-status=live }}</ref> and used his [[Newton's law of universal gravitation|theory of universal gravitation]] to explain the lunar and solar attractions as the origin of the tide-generating forces.{{efn|1=See for example, in the 'Principia' (Book 1) (1729 translation), [https://books.google.com/books?id=Tm0FAAAAQAAJ&pg=PA251 Corollaries 19 and 20 to Proposition 66, on pages 251–254], referring back to page 234 et seq.; and in Book 3 [https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n279 <!-- pg=255 --> Propositions 24, 36 and 37, starting on page 255].}}
Newton and others before [[Pierre-Simon Laplace]] worked the problem from the perspective of a static system (equilibrium theory), that provided an approximation that described the tides that would occur in a non-inertial ocean evenly covering the whole Earth.<ref name=slc-ch2 /> The tide-generating force (or its corresponding [[scalar potential|potential]]) is still relevant to tidal theory, but as an intermediate quantity (forcing function) rather than as a final result; theory must also consider the Earth's accumulated dynamic tidal response to the applied forces, which response is influenced by ocean depth, the Earth's rotation, and other factors.<ref>{{cite book |last=Wahr |first=J. |title=Earth Tides in "Global Earth Physics", American Geophysical Union Reference Shelf #1 |pages=40–46 |date=1995}}</ref>

In 1740, the [[Académie Royale des Sciences]] in Paris offered a prize for the best theoretical essay on tides. [[Daniel Bernoulli]], [[Leonhard Euler]], [[Colin Maclaurin]] and [[Antoine Cavalleri]] shared the prize.<ref name="EulerAiton1996">{{cite book |first1=Leonhard |last1=Euler |author1-link=Leonhard Euler |first2=Eric J. |last2=Aiton |title=Commentationes mechanicae et astronomicae ad physicam pertinentes |url=https://books.google.com/books?id=b1yCADlGTkgC&pg=PR19 |year=1996 |publisher=[[Springer Science+Business Media]] |isbn=978-3-7643-1459-0 |pages=19– |via=[[Google Books]]}}</ref>

Maclaurin used Newton's theory to show that a smooth sphere covered by a sufficiently deep ocean under the tidal force of a single deforming body is a [[prolate]] spheroid (essentially a three-dimensional oval) with major axis directed toward the deforming body. Maclaurin was the first to write about the Earth's [[Coriolis effect|rotational effects]] on motion. Euler realized that the tidal force's ''horizontal'' component (more than the vertical) drives the tide. In 1744 [[Jean le Rond d'Alembert]] studied tidal equations for the atmosphere which did not include rotation.

In 1770 [[James Cook]]'s [[barque]] [[HMS Endeavour|HMS ''Endeavour'']] grounded on the [[Great Barrier Reef]]. Attempts were made to refloat her on the following tide which failed, but the tide after that lifted her clear with ease. Whilst she was being repaired in the mouth of the [[Endeavour River]] Cook observed the tides over a period of seven weeks. At neap tides both tides in a day were similar, but at springs the tides rose {{convert|7|feet}} in the morning but {{convert|9|feet}} in the evening.<ref name=Cook>{{cite journal |editor-last=Thomson |editor-first=Thomas |editor-link=Thomas Thomson (chemist) |title=On Capt. Cook's Account of the Tides |date=March 1819 |publisher=Baldwin, Cradock and Joy |place=London |journal=[[Annals of Philosophy]] |volume=XIII |page=204 |url=https://www.biodiversitylibrary.org/page/15877750 |access-date=25 July 2015 |archive-date=26 August 2016 |archive-url=https://web.archive.org/web/20160826094842/http://biodiversitylibrary.org/page/15877750 |url-status=live }}</ref>

Pierre-Simon Laplace formulated a system of [[partial differential equation]]s relating the ocean's horizontal flow to its surface height, the first major dynamic theory for water tides. The [[Laplace's tidal equations|Laplace tidal equations]] are still in use today. [[William Thomson, 1st Baron Kelvin]], rewrote Laplace's equations in terms of [[vorticity]] which allowed for solutions describing tidally driven coastally trapped waves, known as [[Kelvin wave]]s.<ref name="tidhist">{{cite journal |title=Historical Development and Use of Thousand-Year-Old Tide-Prediction Tables |journal=Limnology and Oceanography |volume=34 |issue=5 |date=July 1989 |pages=953–957 |last1=Zuosheng |first1=Y. |last2=Emery |first2=K.O. |last3=Yui |first3=X. |name-list-style=amp |doi=10.4319/lo.1989.34.5.0953 |bibcode=1989LimOc..34..953Z |doi-access=free}}</ref><ref>{{cite book |title=Tides: A Scientific History |url=https://archive.org/details/tidesscientifich0000cart |url-access=registration |last=Cartwright |first=David E. |publisher=[[Cambridge University Press]] |location=Cambridge, UK |date=1999 |isbn=9780521621458}}</ref><ref>{{cite journal |title=Understanding Tides – From Ancient Beliefs to Present-day Solutions to the Laplace Equations |first=James |last=Case |journal=SIAM News |volume=33 |issue=2 |date=March 2000}}</ref>

Others including Kelvin and [[Henri Poincaré]] further developed Laplace's theory. Based on these developments and the [[lunar theory]] of [[Ernest William Brown|E W Brown]] describing the motions of the Moon, [[Arthur Thomas Doodson]] developed and published in 1921<ref>{{cite journal |last=Doodson |first=A.T. |date=December 1921 |title=The Harmonic Development of the Tide-Generating Potential |journal=Proceedings of the Royal Society of London A |volume=100 |issue=704 |pages=305–329 |bibcode=1921RSPSA.100..305D |doi=10.1098/rspa.1921.0088 |doi-access=free}}</ref> the first modern development of the tide-generating potential in harmonic form: Doodson distinguished 388 tidal frequencies.<ref>{{cite journal |title=A fully analytical approach to the harmonic development of the tide-generating potential accounting for precession, nutation, and perturbations due to figure and planetary terms |journal=[[AAS Division on Dynamical Astronomy]] |date=April 2004 |volume=36 |issue=2 |page=67 |last1=Casotto |first1=S. |last2=Biscani |first2=F. |name-list-style=amp |bibcode=2004DDA....35.0805C}}</ref> Some of his methods remain in use.<ref>{{cite book |last=Moyer |first=T.D. |date=2003 |url=http://descanso.jpl.nasa.gov/Monograph/series2/Descanso2_all.pdf |title=Formulation for observed and computed values of Deep Space Network data types for navigation |archive-url=https://web.archive.org/web/20041016204145/http://descanso.jpl.nasa.gov/Monograph/series2/Descanso2_all.pdf |archive-date=2004-10-16 |volume=3 |series=Deep-space communications and navigation |publisher=[[Wiley (publisher)|Wiley]] |pages=126–128 |isbn=0-471-44535-5}}</ref>