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neither can they always be regarded as spherical triangles; for the plummets at the three angles of the triangle do not all tend to the same point in the interior of the earth; and, in some cases, do not any one of them intersect another. Spheroidal triangles must therefore differ from spherical; and though, in such triangles as usually occur in a trigonometrical survey, the difference is of no account, yet there is one case where it can by no means be neglected. This happens, when the bearings of any obtuse line, or rather arch, with respect to the meridians that pass through its extremities, are known, and also the latitude of one of those extremities, and it is required to find the difference of the longitude of the said extremities, or the angle which the meridians passing through them make with one another at the pole. If the base of this triangle is considerable, and very oblique to the meridians, the directions of gravity at its extremities will not intersect the earth's axis in the same point,-and the difference may be so great that it cannot be neglected in calculation.

These corrections have all been taken into account, and the application of them fully exemplified, in the measurement of the great arch between Dunkirk and Formentera, (the southernmost of the Balearic Isles.) Indeed, the book in which the facts and investigations respecting this measurement have been recorded by the French mathema

ticians, the Base Métrique, is one of the most valuable works which has yet distinguished the beginning of the nineteenth century.

Major Lambton, who, in 1801, proposed the survey of the Peninsula of India, was fully aware of all those new improvements, and perfectly prepared for carrying them into effect. It is indeed much to the credit of the British army, that in a detachment of it, in a distant country, an officer should be found already prepared for a service implying such scientific acquirements, as nothing but the strong impulse of genius could have rendered compatible with the duties or the amusements of a military life.

The plan having been first approved by the governor of Madras, and afterwards communicated to the Asiatic Society, was published in the 7th volume of their Researches. The recent conquest of the Mysore had just opened the interior of the country, and made it practicable to join the coasts of Malabar and Coromandel, by a series of triangles which might be extended on the south, to the extremity of the Peninsula, and to an indefinite distance on the north. It was proposed to execute the work on a plan similar to that pursued in France and England, paying attention to the spherical excess, the spheroidal figure of the earth, and the other circumstances which have just been mentioned. The India Company furnished the Major

with the best instruments that could be procured; and indeed it is but justice to remark, that, in whatever concerns geographical improvement, the liberal and enlarged views of the present rulers of India cannot be too highly commended. * At the present moment, no country in the world, except France and England, has its geography ascertained by a survey so accurate and extensive as that of which we are here to give an account.

The instruments used in the Indian survey, are of the same kind with those employed in the British. The theodolite is one made by Cary, after the model of that invented by Ramsden, and described by General Roy in the Philosophical Transactions for 1790, with some additional improveThe instrument for the celestial observa

ments.

• They have sent out parties, in all directions, for the purpose of ascertaining the bearings and distances of the places which compose or limit their extensive dominions. A late volume of the Asiatic Researches contains an account of the march of an officer, at the head of a detachment, into one of the most remote and unknown districts of India, for no other purpose but to decide a question, interesting only to philosophers, viz. Whether the Ganges rises within or without, that is, on the south or the north side of the great chain of Himmaleh, the Snowy Mountains, or the Immaus of the ancients?-There are but few of the most enlightened cabinets in Europe which can boast of an expedition equally disinterested and meritorious.

tions, was a zenith sector of five feet radius by the same artist; it is capable of ascertaining small fractions of a second, and appears to be an excellent instrument, though not so large as that used in the British survey. The chains employed in the measurement of the bases, were also similar to Ramsden's. That every source of error might, as far as possible, be removed, the angles were usually taken three or four times;-at each time the angle was read off from the opposite microscopes of the theodolite, and the results set down in two separate field-books. The mean of the numbers from the two books, are those employed in the calculation, and recorded in the printed table of observations.

In a survey of the kind here proposed, four separate processes, different in themselves, and directed to distinct objects, are necessary to be combined. The first is the measurement of a base, or of more bases than one, each of which must be a straight and level line, at least five or six miles long. This, it has been usual to measure, by placing straight rods, sometimes of deal, sometimes of metal, or even of glass, all of the same length, one at the end of another, each supported hori zontally along the whole line. It was found by General Roy, that a steel chain, made in a particular manner, somewhat like a watch chain, and stretched in a wooden trough, by weights that are

always the same, is not less to be depended on than the rods, and is far more convenient. This method of measuring the base was employed by Major Lambton, and he considered the base he had measured, conformably to what is before mentioned, as a polygon or a series of chords inscribed in a circle, as many in number as there have been chains. The real base is the circular arch in which these chords are inscribed.

The next part of the process is the formation of a series of triangles which go from hill to hill, over the whole space to be included in the survey, and having the base already measured, for a side of one of them. In each triangle the angles are to be taken, and then, by trigonometry, their sides can be determined: The whole may be laid down on paper; and the position of every point within the survey may be found, with respect to every other. This is sufficient, therefore, for determining the position and magnitude of every line, and every figure, within a given extent; but it does not determine the position of the tract surveyed, in respect of the other parts of the earth's surface. It does not determine its situation in respect of the quarters of the heavens, in respect of the parallels of latitude, or in respect of the different meridians which divide the surface of the globe from north to south. The first of these objects is obtained by observing carefully the azimuths of one or more of

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