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placed centrally over the dots which mark the extremities of that line, and their telescopes are directed to one another until, as it has been graphically said, "they look down the throats of each other." The telescopes being in this position, are clearly both of them directed along the base-line. Each of them being now turned round till it looks straight at the object which has been fixed upon, the instruments are clamped, and the angles through which the telescopes have been turned are read off on the graduated circles. The angles are thus ascertained, which lines, drawn to the object from the extremities of the base, make with the base-line. The object, in short, is made the summit of a triangle in which two angles and the length of the side between them are known. Its distance from either end of the base can thus be ascertained by computation, and made available as a new and larger base. "Thus," says Sir John Herschel, in a paper in which this subject is handled with his usual lucidity,* "the survey may go on, throwing out new triangles on all sides, of larger and larger dimensions, till the whole surface of a kingdom or a continent becomes covered with a network of them, all whose angular points are precisely determined. The strides so taken, moderate at first, become gigantic at last; steeples, towers, obelisks, mountain cairns, and snowy peaks, becoming in turn the stepping-stones for further progress, the distances being only limited by the range of distinct visibility through the haze of the atmosphere." In mapping a country, after the net-work of great triangles has been thrown over it, the great spaces comprehended

*

1866.

"Familiar Lectures on Scientific Subjects," p. 187. Lond.

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by them are filled in by a system of smaller triangles, so as to carry the survey to any degree of minuteness may be required.

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It will have been seen, in regard to the first set of operations, that the chief requisite in measuring baselines is such a measure, bar, rod, or chain as shall have fewest of those qualities, and be least subject to those conditions in the use, which are the sources of errors of measurement; and in regard to the second set of operations, that, as the triangles increase in magnitude, the means of making distant points steadily and distinctly visible are next in practical importance to the excellence of the instruments for measuring angles. It will be seen hereafter that Mr Drummond made most important contributions to geodesical science in regard to each of these sets of operations.

A sufficiently distinct notion has now, it is hoped, been conveyed of the sort of operations in which the Ordnance Survey engineers were engaged-the measuring of base lines on the one hand, and the work of triangulation on the other. Let us now glance at the history of these operations in Britain up to the time when Drummond took a part in them.

That the British Survey is an Ordnance Survey harmonises with the fact, that the first survey conducted in Great Britain had its origin, not in the interests of science and peace, but in the conditions of public safety and the purposes of war. It was begun shortly after the Rebellion of 1745, in a survey of the Highlands of Scotland, the want of an accurate knowledge of the country having been much felt by the king's troops. This survey was conducted by General Roy, with the help of a body of infantry, whose head-quarters were at Fort Augustus. Begun in the Highlands, it was ex

tended over the south of Scotland, but it was done roughly and with imperfect instruments, and the results were never published. Thus it was, however, that practical experience in the art of surveying happened to be possessed in a high degree by military officers, and that, when survey operations on a grander scale and for higher purposes were resolved upon, military officers were naturally called upon to superintend them. A project for a general survey of the country was formed in 1763, but fell aside, to be renewed in 1783. In this *year a representation was made from France to our Government, of the advantages which the science of astronomy would derive from the connection, through trigonometrical measurements, of the Observatories of Greenwich and Paris, and the exact determination of their latitudes and longitudes. The French had by this time carried a series of triangles from Paris to Calais, and what they proposed was that the English should carry a similar series from Greenwich to Dover, when the two might be connected by observations from both sides of the channel. The scheme was approved of by George III., and the English Survey begun by the measurement of an initial base-line at Hounslow Heath by General Roy-the foundation of the triangulation since effected of Great Britain. While, then, the officers who, from the first, superintended the geodesical operations in Great Britain belonged to the Engineers, and had been trained to the work in the interests of war, it is yet true that the British Survey, of which the measurement of Hounslow base was truly the commencement, had its origin in philosophical operations conducted in the interests of science, and directed mainly to the determination of the figure of the earth.

The measures employed in measuring the Hounslow

base were Ramsden's steel chain, 100 feet long; Riga pine wood rods, 20 feet long; and glass rods, 20 feet long, enclosed in wooden cases for protection. These measures were, all of them, liable to expansion and contraction from changes of temperature; while the rods were, moreover, affected by changes of the hygrometer. The rods, it was found, gained th of an inch in length after a week of rain; which on the length of the base would have caused an error of about 45 inches. On the other hand, the chain, while it possessed many good qualities, was attended by not inconsiderable difficulties in the use. The base, however, was as carefully measured as with the instruments it could be, everything being done to prevent or allow for instrumental errors: its length, reduced to the level of the sea, was about 6th miles. A chain of triangles was then carried from the Hounslow base to Dover, connected with the Greenwich Observatory at one end, and at the other with a base of verification, which was next measured with Ramsden's chain at Romney Marsh. This base was about 5 miles long, and differed only by a few inches from its length as determined by triangulation from the Hounslow base. This completed the operations immediately required for the connection of the Observatories of Greenwich and Paris. But the survey of Great Britain, which from the first had been contemplated, being now resolved upon, the triangulation which had so far been made for purely scientific purposes, formed the basis of the survey of Kent and Middlesex. The Hounslow base was remeasured in 1791, General Roy having died in the previous year; and in 1792, and the two following years, the triangulation was extended southwards to the Isle of Wight. In 1794 a base of verification was measured on Salisbury

Plain with the steel chain, and the triangulation thence continued westward along the whole southern coast, till the triangles embraced Dorset, Devon, Cornwall to the Land's End, and even the Scilly Isles. The work had now assumed the distinct character of a national survey, under the direction of Colonel Mudge. By 1800 the larger triangles had in many districts been filled in, and several counties had been mapped. In 1801 the triangles were carried northwards, and a base measured in North Lincolnshire on Misterton Carr, it being part of the director's plan that a new base, for verification, should be measured every hundred miles. By 1806 the triangles embraced part of North Wales, and a base had been measured on Rhuddlan Marsh, near St Asaph.

While these operations were being carried on, others of a more purely scientific nature were conducted by the officers superintending the survey. The direction of the meridian had been determined at Dunnose and Beachy Head as early as 1794, and calculation made of the length of a degree of a great circle perpendicular to the meridian in latitude 50° 41'; great interest being taken at the time in the question, Whether the length of a degree increased in approaching the equator? The direction of the meridian had subsequently been traced far northwards, and in 1811 it was determined to prolong the line into Scotland. The French, who had moved the English to begin the work, were urging them on in its prosecution at once by precept and example. A meridian had been traced through France, and extended by Biot and Arago to the southernmost of the Balearic Isles. This arc it was proposed, with the assistance of the British geodesists, to terminate at Yarmouth. On the other hand, it was proposed that

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