The Anglo-French survey
Late in life, when he was 57, Roy was granted the opportunity to establish his lasting reputation in the world of geodesy. The opening came from a completely unexpected direction. In 1783 the Comte de Cassini addressed a memoir to the Royal Society in which he expressed grave reservations of the measurements of latitude and longitude which had been undertaken at Greenwich Observatory. He suggested that the correct values might be found by combining the Paris Observatory figures with a precise trigonometric survey between the two observatories. Sir Joseph Banks, president of the Royal Society, proposed that Roy should lead the project. Roy accepted with enthusiasm for he saw that apart from the specific measurements proposed the survey could be the first step towards the national survey that he had advocated so often. The whole project is described by Roy in three major contributions to the Philosophical Transactions of the Royal Society in 1785, 1787 and 1790. 
After a preliminary survey by Roy and three other members of the Society on 16th April, they found a suitable location for the starting baseline on Hounslow Heath, between King's Arbour and Hampton Poor-house just over 5 miles to the south-east. A preliminary measurement of the line was carried out with a steel chain prepared by Jesse Ramsden . It was the intention to measure more accurately with a set of three deal rods about 20 ft. in length but their use had to be abandoned because of their susceptibility to lengthen and shorten in wet weather. The deal rods were replaced by one inch thick glass tubes of the same length. The final measurement gives the length of the base as 27404.7 ft. to an accuracy of about 3 inches in 5 miles (or about 1/100,00). The precision of this baseline measurement far exceeded any previous attempts and in recognition Roy was awarded the Copley medal by the Royal Society in 1785 .
The triangulation itself was delayed until 1787 when Ramsden supplied a new theodolite of unsurpassed accuracy: it could measure angles to within one arc second and therefore detect the curvature of the Earth by measuring the spherical excess of the triangles of the survey. By the end of that year he had completed measurements at all but two of the trigonometric stations. Many of the measurements, particularly the cross channel sightings, were taken at night using intense flares (handled by the artillery). Others required the placing of the instrument on church towers, or even on scaffolded steeples, and in their absence it was sometimes necessary to use a specially constructed portable tower some 30 feet high.
The final report of 1790 presents figures for the distance between Paris and Greenwich as well as the precise latitude, longitude and height of the British triangulation stations. Throughout the survey Roy took every opportunity to fix the position of as many landmarks as possible and these formed the basis of the topographic surveys from which new maps could be prepared. Roy died when only three pages of his final report remained to be proofed.
p18 wooden pipes foot in diameter, 4inch bore p14 cassini4 tactless maskelyne's doubts 14 roy lent by the military to a RS project 21 theod arrived july31 1787 21 white lights (short burning flares 28nitre 4sulphur 2 arsenic tri-sulphate)
handled by artillery from seymour16 reverberatory lamps
21 cross channel sights between 23 sept 17oct 21 most operations at night 21 steeples such as lydd, tenterden 21 romney base measured 28535.7 calculated 28533.3 diff 2.4 or 1/12000
hounslow base error (clarke) 2inch in 5 mile or 1/158000 doverC to ND Calais 137449 and by French 137442 d.long paris Green is 2d19m51s
14 roys plans in response to memoire
in prev years had already spotted likely stations saw hounslow as start for other directions
16 hoped triangles might serve as foundation of a general survey
completed cross ch before winter leaving 2 kent stations for next year
17 ramsden delay, cumulative improvements within a fixed price 21 roy forwarded arc requests to Easy In Co
this led to ramsden2
33-36 chap2 connection paris-G 33 mudge-dalby also described operations of 1784-17?? 33 different results in places 34 pipe 6ft long
hts of baseKA 31.265 above HPH 36.1 above thames deal rods changed 0.5inch in 300ft as humiditiy varied glass tubes corrected to 62F corrected to sea level 54ft below HPH (about ?
35 theo could be raised 16' or 32'
lamps/ white lights/ fkags could be 35' high on tripods
35 14 ground stations 9 up-stations
32 triangles only 17 full observed closing errors of the 17 were less than 1sec
36 calculated dunkirk base was 39808.7 (measured 39801.7ft) 36 final results
calculations on plane other problems lat lon heights of stationscalculated. hts some spirit lev others trig elevations
The triangulation, 1787
Roy's measurements (not fully utilised until 1787, when the Paris and Greenwich observatories were properly connected) form the basis of the topographical survey of Middlesex, Surrey, Kent and Sussex. These surveys were made for the most part using the new Ramsden theodolite which Roy had commissioned from Jesse Ramsden, and were the start of the Principal Triangulation of Great Britain. He was finishing an account of this work for the Philosophical Transactions of the Royal Society when he died.