Editing Mason–Dixon line (section)

==Systematic errors and experiments to weigh the Earth==
Mason and Dixon achieved a high level of accuracy in the survey due to the work of [[Nevil Maskelyne]], some of whose instruments they used.<ref name="davies">{{Cite journal|last=Davies|first=R.D|title=A Commemoration of Maskelyne at Schiehallion|journal=[[Quarterly Journal of the Royal Astronomical Society]]|volume=26|issue=3|pages=289–294|bibcode=1985QJRAS..26..289D|year=1985}}</ref> There was keen interest in their work and much communication between the surveyors, Maskelyne and other members of the British Scientific establishment in the [[Royal Society]] in Britain, notably [[Henry Cavendish]].<ref name="journal">Note the comments on Cavendish's speculation in the introductory notes, and the multiple correspondences with Maskelyne in: {{Cite web|last=Mason|first=Charles|author-link=Charles Mason|author2=Dixon, Jeremiah|author-link2=Jeremiah Dixon|title=The Journal of Charles Mason and Jeremiah Dixon 1763–1768|url=http://www.mdlpp.org/pdf/library/JournalofMasonandDixon.pdf|access-date=2011-01-05|archive-date=December 30, 2017|archive-url=https://web.archive.org/web/20171230025832/http://www.mdlpp.org/pdf/library/JournalofMasonandDixon.pdf|url-status=dead}}</ref><ref name="maskelyne_fellowship">[[Nevil Maskelyne]] was elected a [[List of Fellows of the Royal Society|Royal Society Fellow]] on April 27, 1758; see {{Cite web|url=http://royalsociety.org/WorkArea/DownloadAsset.aspx?id=4294972811|format=pdf|publisher=[[Royal Society]]|title=List of Fellows of the Royal Society 1660–2007|volume=K–Z|page=238|year=2007|access-date=2011-01-05|url-status=dead|archive-url=https://web.archive.org/web/20101130205428/http://royalsociety.org/WorkArea/DownloadAsset.aspx?id=4294972811|archive-date=November 30, 2010}}</ref><ref name="cavendish_fellowship">[[Henry Cavendish]] was elected a [[List of Fellows of the Royal Society|Royal Society Fellow]] on May 1, 1760; see {{Cite web|url=http://royalsociety.org/WorkArea/DownloadAsset.aspx?id=4294972811|format=pdf|publisher=[[Royal Society]]|title=List of Fellows of the Royal Society 1660–2007|volume=A–J|page=66|year=2007|access-date=2011-01-05|url-status=dead|archive-url=https://web.archive.org/web/20101130205428/http://royalsociety.org/WorkArea/DownloadAsset.aspx?id=4294972811|archive-date=November 30, 2010}}</ref>

During such survey work, it is normal to survey from point to point along the line and then survey back to the starting point, where if there were no errors the origin and re-surveyed position would coincide.<ref name="natres">{{Cite web|title=Specifications and Recommendations for Control Surveys and Survey Markers|url=http://www.geod.nrcan.gc.ca/publications/specs/index_e.php#ExpectedAccuracy|publisher=[[Natural Resources Canada]]|page=Table E-VI Position Differences |quote=Double run in straight line by helicopter between control spaced at 80 km.|date=December 27, 2007|access-date=2011-01-06|archive-url=https://web.archive.org/web/20110526012704/http://www.geod.nrcan.gc.ca/publications/specs/index_e.php#ExpectedAccuracy|archive-date=May 26, 2011|url-status=dead}}</ref> Normally the return errors would be random{{snd}}i.e. the return survey errors compared to the intermediate points back to the start point would be spatially randomly distributed around the start point.<ref name="taylor">{{cite book|title=An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements|last=Taylor|first=John Robert|url=https://books.google.com/books?id=giFQcZub80oC&pg=PA94|page=94, §4.1 |isbn=093570275X|year=1999|publisher=University Science Books|access-date=2011-01-05}}</ref> Mason and Dixon found that there were larger than expected [[systematic error]]s, i.e. non-[[random error|random]] errors, that led the return survey consistently being in one direction away from the starting point.<ref name="mentzer">{{Cite web|url=https://caf783ab-f4aa-469d-a4ff-2c3a19268299.filesusr.com/ugd/6f029b_b08999b366b24ef79bdbeff2278b80e0.pdf|title=How Mason and Dixon Ran Their Line|last=Mentzer|first=Robert|access-date=2019-12-01}}</ref>

When this information got back to the Royal Society members, Henry Cavendish realised that this may have been due to the gravitational pull of the [[Allegheny Mountains]] deflecting the [[theodolite]] [[plumb-bob]]s and [[spirit level]]s toward them to the west.<ref name="schaffer">{{Cite interview|last=Schaffer|first=Simon|subject-link=Simon Schaffer|date=May 20, 2010 |work=[[BBC Radio 4]]|title=The Cavendish Family in Science}}</ref><ref name="tretkoff"/> Maskelyne then proposed measuring the gravitational force causing this deflection induced by the pull of a nearby mountain upon a plumb-bob in 1772 and sent Mason (who had returned to Britain) on a site survey through central England and Scotland to find a suitable location during the summer of 1773.<ref name="maskelyne">{{Cite journal
| last = Maskelyne
| first = Nevil
| author-link = Nevil Maskelyne
| title = An account of observations made on the mountain Schehallien for finding its attraction
| journal = [[Philosophical Transactions of the Royal Society of London]]
| location = London
| date = January 1, 1775
| volume = 65
| pages = 500–542
| doi = 10.1098/rstl.1775.0050
| quote = Accordingly Mr. [[Charles Mason]], who had been employed on several astronomical occasions by the [[Royal Society]], was appointed to make a tour through the Highlands of Scotland in the summer of the year 1773, taking notice of the principal hills in England which lay in his route either in his going or in his return.
| doi-access = free
}}</ref><ref name="sillitto">{{Cite web
| last = Sillitto
| first = Richard M.
| title = Maskelyne on Schiehallion
| url = http://www.sillittopages.co.uk/schie/schie90.html
| date = October 31, 1990
| quote = The Royal Society agreed to a proposal that it despatch a surveyor, a Mr [[Charles Mason]] whom they had previously employed on astronomical projects, all the way to Scotland and back, to survey likely-looking mountains, and to select a suitable mountain – ideally it should be a steep-sided cone, or a wedge with its apex ridge running W – E and with steep faces to N and S, and separated from the nearest neighbours to N and S by low land. Mr Mason selected for them a mountain at "the centre of Scotland", [[Schiehallion]] – a wedge, with the summit ridge running nearly W – E, 3547 ft above sea level at its western summit, about 3000 ft at the E-end of the ridge; it presents steep faces to the trench to the N which contains Loch Rannoch and Loch Tummel, and to the deep Gleann Mor to the S. [An approximate altitude for Gleann Mor is 1500 feet, and for the land at the same distance to the north of the ridge is 1600 ft.]
| location = [[The Royal Philosophical Society of Glasgow]]
| access-date = 2011-01-03
}}</ref><ref name="stanley">{{Cite book | last = Mackenzie | first = A. Stanley | year = 1900
| title = The Laws of Gravitation: Memoirs by Newton, Bouguer and Cavendish; together with abstracts of other important memoirs
| page = 53
| chapter = Account of Maskelyne's experiments on Schehallien
| location = New York
| publisher = American Book Company
| access-date = 2011-01-03
| chapter-url = https://books.google.com/books?id=O58mAAAAMAAJ&pg=PA59
| quote = In 1772...The proposal was favourably received by the [[Royal Society|Society]], and Mr. [[Charles Mason]] was sent to examine various hills in England and Scotland, and to select the most suitable (32). Mason found the two hills referred to by [[Nevil Maskelyne|Maskelyne]] were not suitable; and fixed upon [[Schiehallion|Schehallien]] in Perthshire as offering the best situation.}}</ref> Mason selected [[Schiehallion]] at which to conduct what became known as the [[Schiehallion experiment]], which was carried out primarily by Maskelyne and determined the density of the Scottish mountain.<ref name="davies"/><ref name="sillitto"/><ref name="stanley"/> Several years later Cavendish used a very sensitive [[torsion balance]] to carry out the [[Cavendish experiment]] and determine the average density of Earth.<ref name="tretkoff">{{Cite web|url=http://www.aps.org/publications/apsnews/200806/physicshistory.cfm|title=This Month in Physics History June 1798: Cavendish weighs the world|last=Tretkoff|first=Ernie|publisher=[[American Physical Society]]|access-date=2011-01-03}}</ref>