User:Peter Mercator/Sandbox

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Gerardus Mercator, Mercator projection, and the concept of atlas[edit]

Gerardus Mercator (1512–1594) was a Flemish/German[1] cartographer with a vast output of wall maps, bound maps, globes and scientific instruments but his greatest legacy was the mathematical projection he devised for his 1569 world map.

The Mercator projection is an example of a cylindrical projection in which the meridians are straight and perpendicular to the parallels. As a result the map has a constant width and the parallels are stretched east-west as the poles are approached. Mercator's insight was to stretch the separation of the parallels in a way which exactly compensates for their increasing length, thus preserving shapes of small regions, albeit at the expense of global distortion. Such a conformal map projection necessarily transforms rhumb lines, sailing courses of a constant bearing, into straight lines on the map thus greatly facilitating navigation. That this was Mercator's intention is clear from the title: Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendate Accommodata which translates as "New and more complete representation of the terrestrial globe properly adapted for use in navigation". Although the projection's adoption was slow, by the end of the seventeenth century it was in use for naval charts throughout the world and remains so to the present day. It's later adoption as the all-purpose world map was unfortunate step.[2]

Mercator spent the last thirty years of his life working on a vast project, the Cosmographia;[3] a description of the whole universe including the creation and a description of the topography, history and institutions of all countries. The word atlas makes its first appearance in the title of the final volume: "Atlas sive cosmographicae meditationes de fabrica mundi et fabricati figura".[4] This translates as Atlas OR cosmographical meditations upon the creation of the universe, and the universe as created, thus providing Mercator's definition of the term atlas. These volumes devote slightly less than one half of their pages to maps: Mercator did not use the term solely to describe a bound collection of maps. His choice of title was motivated by his respect for King Atlas, a mythical king of Mauretania and the son of the globe-bearing [[Atlas (mythology)|Titan}} of the same name.[5]

  1. ^ See the discussion in Gerardus Mercator#The question of nationality.
  2. ^ See the discussion in Mercator projection#Uses
  3. ^ See the discussion in Gerardus Mercator#Duisburg 1552–1594
  4. ^ See the discussion in Gerardus Mercator#atlas1595.
  5. ^ See the preface to the 1595 posthumous section of Mercator's atlas as translated in Sullivan (2000), pp34–38 (PDF pp103–108)

Sullivan, David (2000), A translation of the full text of the Mercator atlas of 1595 (PDF) 

The Anglo-French survey[edit]

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. [1]

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.

++++++++++ Modern locations of end points: Hampton and Heathrow (hamlet),[2] ++++++++++++++

Close[edit]

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

Seymour[edit]

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

Roy1790[edit]

The triangulation, 1787[edit]

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.

Calculation of the results[edit]

  1. ^ Roy 1785, Roy 1787 and Roy 1790.
  2. ^ Sherwood, Philip. (2009) Heathrow: 2000 Years of History. The History Press ISBN 978-0-7509-5086-2, pp. 25–28