TRIGONOMETRICAL SURVEY. The merit of first applying trigonometry to geodetic operations belongs to Willebrord Snell, who in 1017 undertook a survey of Holland, for the double purpose of establishing the geo graphical positions of the principal cities in that country, and measuring a degree of the terrestrial meridian. The method which he followed was the same in principle as that which would be adopted at the present time. Having formed a series of triangles extending over the country, he observed their angles with a quadrant, and computed their sides from a base which was carefully measured with wooden perches on the ground. He also determined the direction of the meridian at Leyden, and observed its inclination to a side of one of his triangles, and thereby obtained the bearings of the different angular points. Lastly, by observing the altitude of the pole star with a five-feet quadrant at Alkmaar, Leyden, and Bergen-op-zoom, he determined the amplitudes of two celestial arcs; and thence deduced the quantities of which he was in quest.
Since that time, trigonometrical or geodetic surveys have been made iu various countries. A general survey of the British Islands, under the direction of the master-general of the Ordnance, was begun in 1791, and has been continued to the present time. The first conductors of this national undertaking were Colonel Williams and Captain (afterwards General) Mudge, of the Royal Engineers, and Mr. Dalby, who had previously assisted General Roy. Were it not for the admirable maps which are from time to time issued from the Ordnance map-office, it might be inferred that the survey had been discontinued during the last thirty years. The operation
has however never been lost sight of. For some years after the last published account, the triangulation was carried on in Scotland, both along the eastern and western coasts. All the Ordnance maps of GreatBritain south of a line from Preston to Hull have been published on a scale of one inch to a mile ; but operations have commenced for publishing the northern section on the magnificent scale of 6 inches to a mile.
In respect to Ireland, the survey of that country was begun about 1818. A base was measured on the banks of Lough Foyle, near Londonderry, with an apparatus differing from any which bad previously been used, and with precautions to ensure accuracy which probably have never been surpassed. Depend ing on this base, a net-work of triangles was established over the whole of Ireland. The topography of Ireland has been completed ; and the angles of the different chains of primary triangles extending over the whole of Scotland and the adjacent islands have now also been observed. The entire map of Ireland has been published on the six-inch scale.
As one of the results of the various trigo. nometrical surveys, we give the following table of the lengths of degrees of latitude and longitude in English feet:— Degree of Degree Latitude. Meridian. Parallel of l 0° 362748.5 365185.8 10 382858.0 359674.0 20 363173.7 343296.4 30 363658.1 316524.3 40 364254.0 280135.0 45 364575.6 258657.3 50 364889.9 235197.9 60 365489.1 183051.6 70 365978.9 125270.5 80 366299.2 63620.1 90 386410.5 0.0