TRIANGULATION is the operation of dividing any portion of the earth's surface into triangles of as large a size as possible, which may be called primary, and which must be afterward subdivided into triangles of a smaller size, forming a great network of sec ondary or subsidiary triangles, which serve as a means of working down from great to less, and finally completing, by a system of scientific checks, an accurate map or delin eation of the region covered by such triangles, forming the geodesical process called a trigonometrical survey. See TRIGONOMETRICAL SURVEY, ORDNANCE SURVEY. The same operation is used in the measurement of an arc of the meridian, for the purpose of ascertaining the length of a degree of latitude or longitude on any part of the earth's surface; but in this case, only primary triangles are necessary, as no topographical detail is required, and the positions of the apexes of the triangles are astronomically fixed in the most careful manner, which is not always done in the triangles of a trigonomet rical survey.
In carrying out a system of triangulation, much judgment and an accurate local knowledge of a country are necessary; and it very often happens that a more extensive range of angles can be obtained from a comparatively low station than from the tops of the highest mountains. The angles of each triangle should be as hear equal as possible, and, unless local circumstances render it unavoidable, very acute or obtuse angles should not be used. The sides of the primary triangles should be as long as can be conveni ently observed, but in practice they vary from SO* m. or more to 4 in., or even less. The angles are generally determined by a large theodolite, of as simple and strong a con struction as possible, which is fixed on the most elevated points of mountain ranges, etc. When the apexes of the triangles are very distant, heliostats, or mirrors reflecting the sun's rays, are often used, and in dark or cloudy weather the Drummond light has been employed. The primary triangles being fixed on the spherical surface of the earth, cer
tain formulae, according to the rules of spherical trigonometry, must be applied to reduce them to the simple calculations for ascertaining, from certain known data, the sides and angles of plain triangles. The whole of those calculations are dependent on the accu rate measurement of a base or fundamental line. The instruments invented by rapt. Drummond, ILE., with which he measured the base-line of the Irish survey at lough Foyle, and which were afterward employed by sir T. Maelear in verifying Lacaille's lase-line on the plains of 3Ialmesbury, in the Cape triangulat ion, appear to have been as nearly perfect as possible. The length of base-lines used in modern surveys varies from 3 to 7 m. ; gen. Roy's original base-line of the English survey was 5.19 miles.
At the end of a large triangulation, a second or testing base-line is always measured at a distance frcm the original one; if the measured length of this agrees with that ascer tained by calculation, it may be considered a proof of the accuracy of the work in gen cull. In the survey of Great Britain by Nudge and Colby, bases of verification were measured for at least every 200 m., except in Scotland, where only one was measured near Aberdeen, The triangles of the English survey have been extended to and connected with those of France, Russia, etc., as far e. as Siberia, and s. to Algeira ; and it is not at all itnprob title that the triangles of the Russian survey will eventually be connected at one side with those of the great survey of India, which already has the apexes of many of its trian gles on the summits of the Th ibetan Himalaya, and to the eastward across Behring's strait, v:ith those of British America and the United States. Sec Yolland's Account of the _Measurement qf the Base of Lough Foyle (Loud. Longmans, 1847); col. Portlock's Life of and art. " Celestial Measurings and Weighings," by sir John Herschel, Good Words (18G4)..