Editing Principal Triangulation of Great Britain

{{short description|1791–1853 geodetic survey of Britain}}
[[File:Clarke principal triangulation of Britain 1860.jpg|thumb|right|upright=1.4|The principal triangulation mesh over Great Britain, Ireland and the Isle of Man.]] 
The '''Principal Triangulation of Britain''' was the first high-precision [[triangulation (surveying)|triangulation]] [[surveying|survey]] of the whole of Great Britain and Ireland, carried out between 1791 and 1853 under the auspices of the [[Board of Ordnance]]. The aim of the survey was to establish precise geographical coordinates of almost 300 significant landmarks which could be used as the fixed points of local topographic surveys from which maps could be drawn. In addition there was a purely scientific aim in providing precise data for geodetic calculations such as the determination of the [[Arc measurement|length of meridian arc]]s and the [[figure of the Earth]]. Such a  survey had  been proposed by [[William Roy]] (1726–1790) on his completion of the [[Anglo-French Survey (1784–1790)|Anglo-French Survey]] but it was only after his death that the  [[Board of Ordnance]] initiated the trigonometric survey, motivated by military considerations in a time of a threatened French invasion. Most of the work was carried out under the direction of [[Isaac Dalby]],  [[William Mudge]] and [[Thomas Frederick Colby]], but the final synthesis and report (1858) was the work of [[Alexander Ross Clarke]]. The survey stood the test of time for a century, until the [[Retriangulation of Great Britain]] between 1935 and 1962.

==History==
{{seealso|Anglo-French Survey (1784–1790)}}
[[File:RamsdenRS theodolite of 1787.jpg|thumb|The first Ramsden theodolite as used by Roy. (Destroyed by bomb damage in 1941.)]]
In the aftermath of the [[Jacobite rising of 1745]], the [[Prince William, Duke of Cumberland|Duke of Cumberland]] (military commander against the rebels){{snd}} advised by Lieutenant-Colonel [[David Watson (British Army officer)|David Watson]], a Deputy Quartermaster-General of the [[Board of Ordnance]]{{snd}} recognised that there was a need for an accurate map of the [[Scottish Highlands]]. Watson initiated the necessary survey in 1747.{{sfnp|Owen|Pilbeam|1992|p=4}} Watson employed William Roy as a civilian assistant to carry out the bulk of the work. Subsequently Roy, having taken a [[Commissioned officer|commission]] in the [[Royal Engineers|Corps of Engineers]] as a "practitioner engineer", and having become a very competent surveyor, proposed (in a memorandum to the king dated 24 May 1766{{sfnp|Hewitt|2010|p=49}}) a national survey which would be a plan for defence at a time when French invasions were threatened.{{efn|The early history of the Ordnance Survey is covered in {{harvtxt|Owen|Pilbeam|1992}} pp 3–14(true), 12–24(pdf), and {{harvtxt|Seymour|1980}} pp. 1–20 (true), 15–35(pdf).}} The proposal was rejected on grounds of expense.{{sfnp|Owen|Pilbeam|1992|p=5}}

Roy continued to lobby for a survey and his ambitions were realised to a certain extent by an unexpected development. In 1783 the [[French Academy of Sciences]] claimed that the latitude and longitude differences between the  [[Royal Observatory, Greenwich]] and the [[Paris Observatory]] were incorrect, and it was proposed (to the  [[Royal Society]]) that the differences could be reconciled by high precision triangulation over the intervening terrain.{{sfnp|Knowles|2003}}  The Royal Society agreed and, jointly with the Board of Ordnance, they invited Roy to oversee the project.<ref>{{cite journal |last1=Gardiner |first1=R. A. |title=William Roy, Surveyor and Antiquary |journal=[[The Geographical Journal]] |date=1977 |volume=143 |issue=3 |pages=446–447 |doi=10.2307/634712 |jstor=634712 |bibcode=1977GeogJ.143..439G |url=https://www.jstor.org/stable/634712 |issn=0016-7398|url-access=subscription }}</ref>

Roy's first task (1784) was to measure a [[Baseline (surveying)|baseline]] between [[Hampton, London|Hampton]] Poor House ({{Coord| 51.4265|-0.3657|display=inline}}) and King's Arbour ({{Coord| 51.4798 |-0.4503|display=inline}}) on [[Hounslow Heath]], a distance of just over 5 miles (8&nbsp;km).{{efn|A full account of the measurement of the Hounslow Heath baseline is given in {{harvtxt|Roy|1785}}. The appendix includes detailed maps and figures.}} This was a painstaking process: three rods each of 20&nbsp;ft. were supported on trestles and the ends aligned to an accuracy of a thousandth part of an inch. The first rod was then carried to the end of the third, an operation to be repeated 1,370 times. The first set of rods, from instrument maker [[Jesse Ramsden]], was made of wood and, in the particularly wet weather of the Summer of 1784, these were found subject to warping and expansion. After delay of two weeks, Ramsden delivered a new set of rods, now made of solid glass tubing. Mounted in rigid wooden boxes with open ends, these had a sprung brass pin mounted against an ivory scale at one end, and this showed when the rods were joined exactly.{{sfnp|Hewitt|2010|pp=76–77}}{{sfnp|Portlock|1853|pp=viii–x}} The final measurement gave the length of the base as {{convert|27404.01|ft}}.<ref>{{cite web |title=William Roy's surveying baseline: the 240th anniversary |url=https://www.ordnancesurvey.co.uk/blog/william-roy-baseline-240th-anniversary |publisher=[[Ordnance Survey]] |access-date=20 February 2025 |date=15 August 2024}}</ref>

[[File:3foottheodoliteramsden.jpg|thumb|The second Ramsden theodolite as purchased by the Board of Ordnance. Now in the [[Science Museum, London]]]] 
For the subsequent triangulation,{{efn|The strategy of the triangulation is outlined in {{harvtxt|Roy|1787}}. The appendix includes detailed maps and figures.}} Roy ordered a new [[theodolite]] from Jesse Ramsden. This [[Ramsden theodolite]], delivered in 1787, for the first time divided angular scales accurately to within a [[arcsecond|second of arc]].{{efn|A full description of the first Ramsden theodolite is given in {{harvtxt|Roy|1790}}. The appendix includes detailed figures.}}{{efn|The theodolite constructed for Roy by Ramsden is called the Royal Society theodolite. See  {{harvp|Insley|2008}} ''The Great Theodolites''}} The theodolite was the largest ever constructed but, despite its massive size, it was carried from London to the Channel coast and employed on hills, steeples and a moveable tower. At each location the angles to other vertices of the triangulation mesh were measured many times, often at night time using newly devised lights. Finally the angle data was used to calculate the sides of the triangles by using [[spherical trigonometry]].{{sfnp|Roy|1790}}

The final results were inconclusive, for triangulation was inferior to the precision of astronomical measurements, but the survey paved the way for all future work in terms of high precision measurements of length and angle, together with the techniques of calculating on an ellipsoidal surface. In his final report, published posthumously, Roy once again pressed for the extension of the survey to the rest of Britain.{{sfnp|Owen|Pilbeam|1992|p=11}} [[Charles Lennox, 3rd Duke of Richmond]],  as [[Master-General of the Ordnance|Master of the Board of Ordnance]] from 1782, viewed Roy's work with great interest. At the same time he was acutely aware that Britain, lacking a national survey, was falling behind the standards of many other European countries. Moreover, the renewed threat of French invasion made him alarmed at  the lack of accurate maps, particularly of the southern counties. Consequently, in 1791, he put into action Roy's plan for the extension of the survey.{{sfnp|Hewitt|2010|pp=94–95}} The catalyst was the sudden availability of a new improved Ramsden theodolite{{efn|The Ramsden theodolite purchase by Richmond is referred to as The Board of Ordnance theodolite.{{sfnp|Insley|2008}} }} which had been intended for the [[East India Company]]. The purchase of this instrument on 21 June 1791 by the Board is taken as the inauguration of the [[Ordnance Survey]].<ref>{{cite web |title=Celebrating 225 years with new (old) maps!} |url=https://www.ordnancesurvey.co.uk/blog/celebrating-225-years-with-a-map/|publisher=Ordnance Survey |date=21 June 2016}} <!-- Although the OS calls this a blog, it is  not a violation of [[WP:BLOGS]] --> </ref> The very next day Richmond appointed [[Isaac Dalby]] as its first employee, with a brief to extend Roy's survey.{{efn|Dalby was a civilian mathematician who had assisted Roy from 1787. See  {{harvtxt|Owen|Pilbeam|1992}} p11(true), 21(pdf), and {{harvtxt|Seymour|1980}} p22(true),36(pdf).}} In the following month Richmond appointed two officers of the [[Royal Artillery]], Major Edward Williams and Lieutenant [[William Mudge]], as directors.{{sfnp|Hewitt|2010|p=104}}

==Re-measurement of the Hounslow baseline==
[[File:General Roys Baseline.jpg|right|thumb|General Roy's baseline: map as about 1935]]
For the 1784 measurement of the original baseline across Hounslow Heath, Roy had ordered three deal rods cut from a new mast in the Admiralty dock yards. These were intended to be used for the precision measurement but Roy also ordered  a 100&nbsp;ft steel chain from Ramsden which could be used for a quick preliminary measurement.<ref>{{harvtxt|Roy|1785}} Section&nbsp;I</ref> The deal rods proved ineffective because of their changes with humidity and they were replaced with glass rods for the final measurement; however Roy observed that the chain itself was just as accurate as the rods.{{sfnp|Roy|1785|pp=454–455}}  For this reason when Richmond ordered Mudge to remeasure the Hounslow base in Summer of 1791, as a first step in extending the triangulation, the survey started by remeasuring the base with two new {{cvt|100|ft}} chains, again made by Ramsden.{{sfnp|Portlock|1853|pp=viii–x}} The second chain was kept unused as a reference against which any stretching of the first would be detected.{{sfnp|Seymour|1980|p=37}}
[[File:Cannon in Roy Grove Hampton.jpg|alt=Cannon in Roy Grove Hampton|left|thumb|South East end of the Baseline]]

The process of measurement was exceedingly precise.{{sfnp|Mudge|Dalby|Williams|1794}} Since the ground was undulating along the length of the base, the measurement was carried out over 26 stages with varying slopes, the chains for any one stage being constrained to a perfectly straight line by many intermediate supports. These hypotenuse measurements were then projected to the horizontal. Furthermore, the temperature varied from day to day and each measurement was corrected to the length that a chain would take at {{cvt|62|F|C}}. Finally, the length of the base was reduced to its projection at sea level using the height of the south base above the Thames and the fall in the Thames down to its estuary.{{sfnp|Welfare|2023|p=217}} The final result was approximately {{convert|2.75|in}} less than that of Roy;{{sfnp|Portlock|1853|pp=viii–x}} the mean value of {{cvt|27,404.2|ft|2}} was taken for the baseline.{{sfnp|Welfare|2023|p=254}} The modern value, derived from [[GPS]], is {{cvt|27,376.8|ft|m}},{{sfnp|Hewitt|2010|p=78}}{{dubious|GPS measures an ellipsoid|date=February 2025}} a difference of {{cvt|27.4|ft|m}}.{{efn|Roy and Mudge treated their measurements as [[hypotenuse]]s, which they then [[Map projection|projected]] onto an horizontal [[Euclidean plane|plane]] at sea level. GPS uses [[WGS84]] 3-dimensional coordinates:&nbsp;{{cite web |title=A guide to Coordinate systems in Great Britain |url=https://www.ordnancesurvey.co.uk/documents/resources/guide-coordinate-systems-great-britain.pdf|publisher=Ordnance Survey |page=21}}}}
{{clear}}

==Corrections==
[[File:Cannon used as the start of the first OS baseline - geograph.org.uk - 1284869.jpg|thumb|The south-west end of the "Salisbury Base" was marked with a cannon, mounted vertically in the ground. On Ordnance Survey published maps it is shown as "Gun, end of base"<ref>{{cite map |author = |title = Salisbury 208|series="One Inch"|year =1898 |url = https://maps.nls.uk/geo/explore/#zoom=16&lat=51.09640&lon=-1.79522&layers=1&b=1&marker=51.098889,-1.784167|publisher =Ordnance Survey  }}</ref>]]
As the survey proceeded westwards, Mudge decided  to check its accuracy by measuring a new baseline between two points established by the triangulation. He chose [[Salisbury Plain]], measuring between a point near [[Old Sarum Castle]] ({{Coord|51.0955|-1.7984|display=inline}}) and Beacon Hill, near [[Bulford]] ({{Coord|51.1835|-1.7221|display=inline}}), in June 1794. The difference between the distance calculated by triangulation and that established by measurement was less than one inch (over a length of more than seven miles).{{sfnp|Portlock|1853|pp=viii–x}} The result verified not only the accuracy of the triangulation, but also the measurement of the original baseline on Hounslow Heath.{{sfnp|Hewitt|2010|p=141}} After remeasurement in 1849 the "Salisbury Base" (rather than the original base on Hounslow Heath) provided the baseline for subsequent triangulation.<ref>{{cite book |editor1-last=Knight |editor1-first=Charles |editor1-link=Charles Knight (publisher) |title=[[English Cyclopaedia|Cyclopædia of Arts and Sciences]] |date=1861 |publisher=Bradbury and Evans |location=London |page=346|volume=IV|oclc=14175638}}</ref>

During subsequent triangulation, errors due to atmospheric refraction,{{sfnp|Mudge|1801|p=182&nbsp;|ps="[…] determining in a more accurate manner than had yet been done […] the refractive power of air"}} deflection of [[plumb bob|plumb-bobs]],{{sfnp|James|1858|p=575&nbsp;|ps="On the Deflection produced by given masses"}} temperature,{{sfnp|James|1858|pp=200-203&nbsp;|ps="Compensation bars"}} and the spherical nature of the earth (meaning there were [[Spherical geometry|more than 180 degrees in a triangle]]{{sfnp|Todhunter|1873|p=174}}) were all allowed for.
==New national triangulation==
In 1909 it was decided that, because of improvements in the design of [[theodolite]]s, a test of angles recorded in the previous triangulation was necessary. The baseline at [[Lossiemouth]], Morayshire, was selected. The length of the base (measured using the new [[Invar|invar steel]] tapes) was found to correspond satisfactorily with the previous value obtained through triangulation, and that any new survey would not vary significantly from the one completed in the previous century. In 1935, however, General [[Malcolm MacLeod (British Army officer)|Malcolm MacLeod]], OS director, decided that a new national triangulation, the [[Retriangulation of Great Britain]], was required. This was not because of any deficiency in the existing principal triangulation, but because some secondary, local triangulations were not of a standard where they could be reconciled within the existing national framework.{{sfnp|Seymour|1980|pp=214, 268}}

==See also==

* [[Ordnance Survey]]
* [[Ordnance Survey Drawings]]
* [[Great Trigonometrical Survey]] (Indian subcontinent)
* [[Public Land Survey System]] (United States)

==Notes==
{{notelist}}

==References==

{{reflist}}

==Bibliography==
{{refbegin |indent=yes}}
* {{cite book |first=Rachel |last=Hewitt |date=2010 |title=Map of a Nation |location=London |publisher=Granta |isbn=978-1-84708-254-1 |oclc=
743473376}}
*{{cite conference
|title=The Tale of the Great Theodolites
|first=Jane    |last=Insley    |year =2008
|conference=Working Week on ''Integrating the Generations''.
|location= Sweden
|url=http://www.fig.net/pub/fig2008/papers/hs03/hs03_01_insley_2838.pdf
}}
*{{cite book |last1=James |first1=Henry |author1-link=Henry James (British Army officer) |title=Ordnance Trigonometrical Survey of Great Britain and Ireland, Account of the Principal Triangulation |date=1858 |publisher=[[Ordnance Survey]] |location=Southampton, England }}
*{{cite journal
|title=The French Connexion – Between English and French Map Surveys
|last=Knowles    |first=Michael        |year =2003
|journal=Proceedings of the Bath Royal Literary and Scientific Institution (BRLSI) 
|volume=7
|url=http://www.brlsi.org/proceedvol7/Astronomy200301.
|archive-url=https://web.archive.org/web/20071018222953/http://www.brlsi.org/proceedvol7/Astronomy200301.
|archive-date=2007-10-18
}}
*{{cite journal
|date = 1794
|last1 = Mudge    |first1 =William 
|last2 = Dalby    |first2 = Isaac 
|last3 = Williams |first3 = Edward
|title = An Account of the Trigonometrical Survey Carried on in the Years 1791, 1792, 1793, and 1794
|journal = Philosophical Transactions of the Royal Society
|volume = 84    |pages = 414–622
|url =https://archive.org/details/philtrans00785875 
|doi=10.1098/rstl.1795.0023
|doi-access = free
|via=Archive.org}}
*{{cite book 
 |last1=Mudge   |first1=William  |year=1801
 |title=An account of the operations carried out for accomplishing a trigonometrical survey of England and Wales . Volume II, 1797–1799
 |url=https://archive.org/details/bub_gb_wWcOAAAAYAAJ_2 
|publisher=W. Faden
|oclc=10644787
}}
*{{cite book |last1=Portlock |first1=Joseph Ellison |author1-link=Joseph Ellison Portlock |title=The Duties of the Corps of Royal Engineers |date=1853 |publisher=John Wheal |location=London |chapter=Memoir of the late Major-General Colby, Royal Engineers |volume=III}}
*{{cite book
|year=1992 |first1=Tim  |last1=Owen  |first2=Elaine |last2=Pilbeam
|title=Ordnance Survey, map makers to Britain since 1791
|page=
|publisher=Ordnance Survey (HMSO)
|location=Southampton
|isbn=9780319002490
|url=
|oclc=28220563
}}
*{{cite journal
|year = 1785
|last = Roy
|first =William
|title =An Account of the Measurement of a Base on Hounslow-Heath
|journal = Philosophical Transactions of the Royal Society of London
|volume =75   |pages =385–480
|url =https://archive.org/details/philtrans01222507
|doi=10.1098/rstl.1785.0024
|doi-access =free
}}
*{{cite journal
|year = 1787
|last = Roy
|first =William
|title =An Account of the Mode Proposed to be Followed in Determining the Relative Situation of the Royal Observatories of Greenwich and Paris. 
|journal = Philosophical Transactions of the Royal Society of London
|volume =77   |pages =188–226
|url =https://archive.org/details/philtrans08537735
|doi=10.1098/rstl.1787.0019
|s2cid = 186214773
}}
*{{cite journal
|year = 1790
|last = Roy
|first =William
|title =An Account of the Trigonometrical Operation, Whereby the Distance between the Meridians of the Royal Observatories of Greenwich and Paris Has Been Determined 
|journal = Philosophical Transactions of the Royal Society of London
|volume =80    |pages =111–254 
|url =https://archive.org/stream/philtrans00940584/00940584#page/n0/mode/2up
|doi=10.1098/rstl.1790.0015
|s2cid = 186211548
}}
*{{cite book |title=A History of the Ordnance Survey |editor-last=Seymour |editor-first=W.A. |year=1980 |location=Folkestone |publisher=Wm Dawson & Sons |url=https://www.ordnancesurvey.co.uk/documents/resources/os-history.pdf |access-date=11 December 2023 }}
*{{cite book |last1=Todhunter |first1=Isaac |author1-link=Isaac Todhunter |title=A history of the mathematical theories of attraction and the figure of the earth from the time of Newton |date=1873 |publisher=[[Macmillan Publishers|Macmillan]] |location=London |oclc=833751892 |volume=II}}
*{{cite book |last=Welfare |first=Humphrey |author-link=|date=2023 |title=General William Roy, 1726-1790 Father of the Ordnance Survey|publisher=Edinburgh University Press|isbn= 9781399505802}}

{{refend}}

==Further reading==
*{{cite book
|year=1858
|first1=Alexander Ross   |last1=Clarke
|first2=Henry                 |last2=James
|authorlink=Alexander Ross Clarke
|authorlink2=Henry James (British Army officer)
|title=Account of the observations and calculations of the Principal Triangulation; and of the figure, dimensions and mean specific gravity of the Earth as derived therefrom.
|publisher=G.E. Eyre and W. Spottiswoode
|location=London
|url=https://books.google.com/books?id=pHTlAAAAMAAJ&q=Account+of+the+observations+and+calculations+of+the+Principal+Triangulation
|oclc=757179661
|via=Google Books
}}
*{{cite journal
|year = 1797
|last1 = Mudge    |first1 =William 
|last2 = Dalby    |first2 = Isaac 
|last3 = Edward |first3 =Williams
|title = An Account of the Trigonometrical Survey Carried on in the Years 1795–1796
|journal = Philosophical Transactions of the Royal Society
|volume = 87    |pages = 432–541
|url =https://archive.org/details/philtrans01773715
|doi=10.1098/rstl.1797.0022
|doi-access = 
|s2cid = 186212662
|via=Archive.org}}
*{{cite book
 |last1=Mudge   |first1=William   |last2 = Dalby |first2 = Isaac   |year=1799
 |title=An account of the operations carried out for accomplishing a trigonometrical survey of England and Wales . Volume I, 1784–1776
|oclc=10644787
 |url=
|publisher=W. Faden
}}

*{{cite journal
|year = 1800
|last = Mudge    |first =William 
|title = An Account of the Trigonometrical Survey Carried on in the Years 1797–1799
|journal = Philosophical Transactions of the Royal Society
|volume = 90    |pages = 539–728
|url =https://archive.org/details/jstor-107063
|doi=10.1098/rstl.1800.0021
|doi-access = free
|via=Archive.org
}}
*{{cite journal
|year = 1803
|last = Mudge    |first =William 
|title = Account of the Measurement of an Arc of the Meridian from Dunnose, Isle of Wight, to Clifton in Yorkshire
|journal = Philosophical Transactions of the Royal Society
|volume = 93    |pages = 383–508
|url =http://rstl.royalsocietypublishing.org/content/93/383.full.pdf+html?sid=dc84cc2f-12fd-4e21-9c68-0763800409c8
|doi=10.1098/rstl.1803.0016
|url-access = subscription
}}*{{cite book 
 |last1=Mudge   |first1=William|  last2=Colby|first2=Thomas    |year=1811
 |title=An Account of the Trigonometrical Survey carried on by Order of the Master-General of His Majesty's Ordnance. Volume III, 1800–1809
 |url=https://books.google.com/books?id=0e9eAAAAcAAJ&pg=GBS.PR1
|publisher=W. Faden
|oclc=10644787
}}
*{{cite journal |author=Lieut.-Colonel T. Pilkington White |url=http://gdl.cdlr.strath.ac.uk/smcj/smcj011/smcj0111001.htm |title=The Ordnance Survey Of The United Kingdom |journal=Scottish Mountaineering Club Journal |date=1886 |volume=2 |number=5|page=170 |doi=10.1038/035170c0 |bibcode=1886Natur..35R.170. |s2cid=101687 }}

==External links==
* [http://www.osni.gov.uk/downloads/grid.pdf PDF file including history and map of the Irish part and its links to Britain]
* [http://www.trigtools.co.uk Information and Maps] on many aspects of [[Triangulation]] (& Levelling) in Great Britain
* {{cite web |url=http://www.remuseum.org.uk/rem_his_history.htm |title=History Section - Corps History |website=Royal Engineers Museum |archive-url=https://web.archive.org/web/20060829135946/http://www.remuseum.org.uk/rem_his_history.htm |archive-date=2006-08-29 |via=Archive.org}} 
* {{cite web |url=http://www.remuseum.org.uk/biography/rem_bio_roy.htm |title=	Major General William ROY (1726-1790)|website=Royal Engineers Museum |archive-url=	https://web.archive.org/web/20060829140407/http://www.remuseum.org.uk/biography/rem_bio_roy.htm|archive-date=	2006-08-29|via=Archive.org}} 

{{Atlas}}

{{DEFAULTSORT:Principal Triangulation Of Great Britain}}
[[Category:Cartography]]
[[Category:Geography of the United Kingdom]]
[[Category:Historical geography of the United Kingdom]]
[[Category:1784 in Great Britain]]
[[Category:Maps of the United Kingdom]]
[[Category:Geodetic surveys]]
[[Category:Surveying of the United Kingdom]]