Principal Triangulation of Great Britain

In addition there was a purely scientific aim in providing precise data for geodetic calculations such as the determination of the length of meridian arcs and the figure of the Earth.

In the aftermath of the Jacobite rising of 1745, the Duke of Cumberland (military commander against the rebels) – advised by Lieutenant-Colonel David Watson, a Deputy Quartermaster-General of the Board of Ordnance – recognised that there was a need for an accurate map of the Scottish Highlands.

[5] Roy's first task (1784) was to measure a baseline between Hampton Poor House (51°25′35″N 0°21′57″W / 51.4265°N 0.3657°W / 51.4265; -0.3657) and King's Arbour (51°28′47″N 0°27′01″W / 51.4798°N 0.4503°W / 51.4798; -0.4503) on Hounslow Heath, a distance of just over 5 miles (8 km).

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.

[d][e] 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.

[10] Charles Lennox, 3rd Duke of Richmond, as 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.

[14] 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.

As the survey proceeded westwards, Mudge decided to check its accuracy by measuring a new baseline between two points established by the triangulation.

[22] During subsequent triangulation, errors due to atmospheric refraction,[23] deflection of plumb-bobs,[24] temperature,[25] and the spherical nature of the earth (meaning there were more than 180 degrees in a triangle[26]) were all allowed for.