The first operation was the laying out of a base line and Roy selected Hounslow Heath as a suitable location, not only for the southeast of England but also with an eye to extending the survey to the rest of the country. Starting on 16 Apr 1784 and continuing through the summer, a length of 27,404.72 feet (about 5 miles) was set out and measured three times - using cased glass tubing made by Ramsden, seasoned deal rods and a coffered steel chain made by Ramsden. The glass tubing was considered to be the most accurate, but the three measurements agreed to within three inches and the steel rods were later adopted as standard.
Sightings from the ends of the baseline to St Ann’s Hill (Chertsey) and Hanger Hill Tower gave another calculated baseline for the triangulations to Severndroog Castle (near Greenwich) and Hundred Acre (Banstead), then quadrilaterals through Frant to Hastings (Fairlight Down), and Hollingbourne Hill (Maidstone) to Allington Knoll and Dover Castle.
The triangulation was completed in 1789. In 1787, the survey had reached the coast and a line was measured on Romney Marsh using Ramsden's steel chain and the measured length agreed with the calculated length to within a foot. Roy had estimated the cost of the triangulation as £1,000, but over £2,000 was spent.
The Hounslow Heath base line was resurveyed in 1791 by Captain Williams, Mudge and Dalby, obtaining a value only 2 inches different and the average was accepted as the basic measurement.
Roy's work led to the foundation of the Ordnance Survey in 1791
In 1791, the original wooden pipes marking the ends of the base line were found to already be decayed and they were replaced by guns buried vertically. Bronze plates were attached to the guns in 1926 to commemorate the bicentenary of Roy's birth. The northwest gun was removed in 1944 due to expansion of Heathrow Airport. It was returned to its original position in 1972. The southeast gun has never been moved and is in Roy Grove, Hampton - grid reference TQ 137709.
The "Principal Triangulation" begun by Roy continued until 1835, but was eventually superseded by a re-triangulation begun in 1935, and completed in 1962. This involved erecting concrete pillars (trig points) on hilltops throughout Great Britain. The re-triangulation was the basis of the British national grid reference system, and new Ordnance Survey maps.
Edited from http://www.dcs.warwick.ac.uk/bshm/zingaz/LondonPeopleN.html#roy, http://www.brlsi.org/proceedvol7/Astronomy200301.htm, and http://en.wikipedia.org/wiki/Retriangulation_of_Great_Britain
See also http://www.twickenham-museum.org.uk/detail.asp?ContentID=276 and a biograhpy of Roy, at http://www.remuseum.org.uk/biography/rem_bio_roy.htm