Editing John Couch Adams (section)

==Lunar theory – Secular acceleration of the Moon==
Since ancient times, the [[Moon]]'s mean rate of motion relative to the stars had been treated as being constant, but in 1695, [[Edmond Halley]] had suggested that this mean rate was gradually increasing.<ref>{{cite journal|author=Halley, Edmond |title=Some Account of the Ancient State of the City of Palmyra, with remarks on the Inscriptions found there|journal=Philos. Trans. R. Soc. |year=1695 |volume=218|pages=160–175|doi=10.1098/rstl.1695.0023 |jstor=102291|s2cid=186214936|url=https://archive.org/details/philtrans06532945|doi-access=free}} Also Philos. Trans. R. Soc. (Abridgements) vol. 4 (1694–1702) pp. 60 at 65:  Halley concluded his 1695 article on middle-eastern antiquities by writing: "And if any curious traveller ... would please to observe, with due care, the phases of the moon's eclipses at Bagdat, Aleppo and Alexandria, thereby to determine their longitudes, they could not do the science of astronomy a greater service: for in and near these places were made all the observations by which the mean motions of the sun and moon are limited: and I could then pronounce in what proportion the moon's motion does accelerate; which that it does, I think I can demonstrate."  But it was left to [[Richard Dunthorne]] actually to make the first quantitative assessment of the Moon's apparent acceleration.</ref> Later, during the eighteenth century, [[Richard Dunthorne]] estimated the rate as +10" (arcseconds/century<sup>2</sup>) in terms of the resulting difference in lunar longitude,<ref>{{cite journal|author=Dunthorne, Richard |year=1749|doi=10.1098/rstl.1749.0031|title=A Letter from the Rev. Mr. Richard Dunthorne to the Reverend Mr. Richard Mason F.R.S. and Keeper of the Wood-Wardian Museum at Cambridge, concerning the Acceleration of the Moon|journal=Philosophical Transactions |volume=46 |issue=492|pages=162–172|bibcode=1749RSPT...46..162D|s2cid=186210495|doi-access=free}}<br />{{snd}} also given in Philosophical Transactions (abridgements) (1809), [https://archive.org/stream/philosophicaltra09royarich#page/669/mode/2up vol. 9 (for 1744–49), pp. 669–675] as "On the Acceleration of the Moon, by the Rev. Richard Dunthorne".</ref> an effect that became known as the ''secular acceleration of the Moon''. [[Pierre-Simon Laplace#Planetary and lunar inequalities|Pierre-Simon Laplace]] had given an [[Lunar theory|explanation]] in 1787 in terms of changes in the [[Equation of time#Eccentricity of the Earth's orbit|eccentricity of the Earth's orbit]]. He considered only the radial gravitational force on the Moon from the [[Sun]] and Earth but obtained close agreement with the historical record of observations.<ref>{{cite book | title=Orbital Motion | url=https://books.google.com/books?id=Hzv7k2vH6PgC&pg=PA313 | page=313 | author=Roy, A.E. | date=2005 | publisher=CRC Press | isbn=0-7503-1015-4 | location=London }}</ref>

In 1820, at the insistence of the ''[[Académie des sciences]]'', Damoiseau, Plana and [[Francesco Carlini]] revisited Laplace's work, investigating [[quadratic function|quadratic]] and higher-order perturbing terms, and obtained similar results, again addressing only a radial, and neglecting tangential, gravitational force on the Moon. Hansen obtained similar results in 1842 and 1847.<ref name="gold">{{cite journal | url=http://adsabs.harvard.edu//full/seri/MNRAS/0026//0000157.000.html | title=Address on award of RAS gold medal for work on secular acceleration of the Moon | journal=Monthly Notices of the Royal Astronomical Society | volume=26 | date=1866 | page=157 | author=de la Rue, W. | author-link=Warren de la Rue |bibcode = 1866MNRAS..26..157.}}
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In 1853, Adams published a paper<ref>{{cite journal | title=On the secular variation of the Moon's mean motion | author= Adams, J.C. | journal=Philosophical Transactions of the Royal Society of London | volume=143 | date=1853 | pages=397–406  | doi=10.1098/rstl.1853.0017| s2cid= 186213591 | doi-access= }}</ref> showing that, while tangential terms vanish in the first-order theory of Laplace, they become substantial when quadratic terms are admitted. Small terms [[integral|integrated]] in time come to have large effects and Adams concluded that Plana had overestimated the secular acceleration by approximately 1.66" per century.<ref name="gold"/>

At first, Le Verrier rejected Adams's results.<ref name="kushner">{{cite journal | author=Kushner, D. | date=1989 | title=The controversy surrounding the secular acceleration of the moon's mean motion | journal=Archive for History of Exact Sciences | volume=39 | pages=291–316 | issue=4|bibcode = 1989AHES...39..291K | doi = 10.1007/BF00348444|url=https://link.springer.com/article/10.1007/BF00348444 |jstor=41133856| s2cid=116653391 }}</ref> In 1856, Plana admitted Adams's conclusions, claiming to have revised his own analysis and arrived at the same results. However, he soon recanted, publishing a third result different both from Adams's and Plana's own earlier work. Delaunay in 1859 calculated the fourth-order term and duplicated Adams's result leading Adams to publish his own calculations for the fifth, sixth and seventh-order terms. Adams now calculated that only 5.7" of the observed 11" was accounted for by gravitational effects.<ref name="gold"/> Later that year, Philippe Gustave Doulcet, Comte de Pontécoulant published a claim that the tangential force could have no effect though [[Peter Andreas Hansen]], who seems to have cast himself in the role of [[arbitrator]], declared that the [[Legal burden of proof|burden of proof]] rested on Pontécoulant, while lamenting the need to discover a further effect to account for the balance. Much of the controversy centred around the [[Convergent series|convergence]] of the [[power series expansion]] used and, in 1860, Adams duplicated his results without using a power series. Sir [[Sir John Lubbock, 3rd Baronet|John Lubbock]] also duplicated Adams's results and Plana finally concurred. Adams's view was ultimately accepted and further developed, winning him the [[Gold Medal of the Royal Astronomical Society]] in 1866.<ref name="eb"/><ref name="gold"/><ref name="kushner"/> The unexplained drift is now known to be due to [[tidal acceleration]].<ref name="ODNB"/>

In 1858 Adams became professor of mathematics at the [[University of St Andrews]], but lectured only for a session, before returning to Cambridge for the Lowndean professorship of astronomy and geometry.  Two years later he succeeded Challis as director of the [[Cambridge Observatory]], a post Adams held until his death.<ref name="eb"/>