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 improvements. The instrument for the celestial observations, 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 horizontally 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 hea

vens, 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 the sides of the triangles, that is, their bearings with respect to the meridian. This serves to place the whole in its due direction with respect to the cardinal points, or to orient the plan, if we may borrow a term from the French, which we wish we had weight enough to introduce into our own language. *

The next thing to be done, is to place the tract surveyed between the same two parallels of latitude, on the artificial globe which it actually lies between, on the surface of the earth. This is done, by observing the latitude at any two stations in the survey, at a considerable distance north or south from one another. If, when this is performed, the distance between the two places reduced to the direction of the meridian be computed, we have the measure of a degree; which, therefore, is a thing almost necessarily implied in a trigonometrical survey.

The position of the whole then, as to its distance from the equator, or from the pole, is thus found; but its distance east or west, from some given meridian, that is to say, its longitude, remains to be determined; and this must be settled by the comparison of the time in some point within the survey, with the time as reckoned under the given meridian. To all these objects Major Lambton has directed his observations, and, we think, with remarkable success.

The base was measured on a plane near Madras, at no great distance from the shore, and nearly on the level of the sea, in spring 1802. The length of the base, reduced to the level of the sea, and to the temperature of 62°, is 40006.44 feet, or 7.546 miles; the latitude of the north end was 13° 0' 29", (Asiatic Researches, Vol. VIII. p. 149, &c.); and it made an angle of little more than 12' with the meridian. From this a series

* We want very much a verb to denote the act of determining the position of a line, or a system of lines, in respect of the quarters of the heavens. The French use the word orienter for this purpose; and we propose to translate this by the phrase to orient. The English language is remarkably poor in words denoting position in respect of the heavens. Our sailors have been obliged to borrow the harsh term, rhumb, from the Portuguese; to denote, by a single word, the point of the compass on which a ship sails. In Scotland they use the word airth, or airt, for the same purpose; and sometimes convert it into a verb, to airt, orienter, or to orient. The Scots term, however, is neither of so good a sound, or so classical an origin, as that which we propose to introduce.

of triangles was carried, about 85 miles eastward, north as far as the parallel of 13° 19′ 49′′ N., and south to Cuddalore, latitude 11° 44′ 53", embracing an extent of about 3700 square miles. The triangles seem well contrived for avoiding very acute and very obtuse angles; the sides of many are from 30 to 40 miles in length, which indicates a fine climate, where the air is very transparent, and a country where hills of considerable elevation are easy to be found. In computing the sides, Major Lambton reduced the observed angles to the angles of the chords, according to the method of De Lambre; and though he computed the spherical excess, he did not use it in any other way than as a measure of the accuracy of his observations. The knowledge of this spherical excess enables one, from having two angles of a spherical triangle, such as occurs in the survey, to find the third, though it be not observed. This is a facility of which a careful observer will avail himself as seldom as possible, as it deprives him of the check by which the errors in the angles might be detected. The difficulty of the country often proves a temptation to make use of it in this way, so as to avoid the necessity of carrying the theodolite to the more inaccessible points. Major Lambton has no appearance of a person who would save labour at the expense of accuracy; and, whenever he has omitted to take all the three angles of a triangle, we believe that it has arisen from the necessity of the case. The chords, which were the sides of the triangles, were then con verted into arches; and as by a very judicious arrangement, which, however, is not always practicable, Major Lambton had contrived, that the sides of the four triangles which connected the stations at the south and north extremities should lye very nearly in the direction of the meridian, their sum, with very little reduction, gave the length of the intercepted arch, which was thus found to be 95721.326 fathoms

By a series of observations for the latitude, at the extremities of this arch made with the zenith sector above mentioned, the amplitude of the arch was found to be 10.58233, by which, dividing the length of the arch just mentioned, Major Lambton obtained 60494 fathoms for the degree of the meridian, bisected by the parallel of 12° 32'. This, till the survey was extended farther to the south, was the degree nearest to the equator, (except that in Peru, almost under it,) which had yet been measured, and was, on that account, extremely interesting.

The next object was to measure a degree perpendicular to the meridian, in the same latitude. This degree was accordingly derived from a distance of more than 55 miles, between the stations at Carangooly and Carnatighur, nearly due east and west of one

or other. Very accurate measures of the angles, which that line made with the meridian at its extremities, were here required; and these were obtained, by observations of the Pole star, when at its greatest distance from the meridian. For this purpose, a lamp was lighted, or the blue lights were fired at a given station, the azimuth of which was found by the Pole star observations, and afterwards its bearing in respect of the line in question. Thus the angle which the meridian of Carangooly makes at the pole, with that of Carnatighur, or the difference of longitude of these two places, was computed. It was then easy to calculate the amplitude of the arch between them; and thence the degree perpendicular to the meridian at Carangooly, was found to be 61061 fathoms.

With regard to the measure of this perpendicular degree, we confess that we do not see reason to place great confidence in it, notwithstanding our high opinion of the observer. The me thod of determining the difference of longitude, by the convergency of the meridians, or the angles they make with a line intersecting them, is not easily applicable in low latitudes, or in places near to the equator; because there, a very small error in the observation of the azimuths, must produce a very great one in the difference of longitude. The convergency of the meridians is so small, in the present instance, that if a line were to be drawn through Carangoly parallel to the meridian of Carnatighur, it would not make with the former an angle of one minute. A very small error, therefore, in ascertaining the angle which these lines make with a third line, must greatly affect the quantity of the angle which they make with one another. This is also evident from considering, that at the equator, all the me ridians make right angles with the line from east to west, and have therefore no convergency at all. The problem of determining the difference of the longitude, or the arch of the equator, by the angles which it makes with the meridian, comes here under the porismatic or indeterminate case, where the data can lead to no definite conclusion. This is evidently true at the equator; and we are constantly coming nearer to this condition of things, as we come nearer to that circle. The porismatic case of a problem, like every other, does not arise all at once, but comes on by gradations; every approach to the state in which the thing sought is quite indeterminate, being marked by the greater looseness and inaccuracy of the determination actually given.

Of the degree of the perpendicular as here given, viz. 61061 fathoms, we have farther to remark, that when compared with the degree of the meridian, it brings out the compression at the

poles equal to, which is certainly much too great. But if it be diminished by 200 fathoms, and reduced to 60861, as an ingenious writer (Phil. Trans. 1812, p. 342) contends that it ought to be, on account of an error in calculation, which has escaped Major Lambton, it gives for the compression, which is probably not far from the truth.

The measures of which we have been giving an account, were made in 1803; the next, of which we are informed in the tenth volume, were in 1806, when the series of triangles was carried quite across the Peninsula to the Malabar coast, which they intersected at Mangalore on the north, and Tillicherry on the south. In this tract they of course passed over the Ghauts, so remarkable both in the natural and civil history of Hindostan; and as the stations, most probably, are the tops of some of the highest mountains, their heights may serve to give some idea of the general elevation of the chain. The most considerable are, Soobramance and Taddiandamole, in the western Ghaut, not very far from the coast, the former 5583 feet, and the latter 5682 above the level of the sea. Considerable difficulty could not fail to be experienced in conducting the survey across these mountains.

I had laid (says the Major) the foundation for a southern series of triangles, to be carried through the Koorg, to mount Delli, (on the coast), which was rendered practicable by the assistance afforded me by the Koorg Rajah, to whose liberal aid I am indebted for the successful means I had in carrying the triangles over those stupendous mountains.' Vol. X. p. 295.

The heights of the stations were all determined from the distances and observed angles of elevation; and it is no small proof of accuracy, that after ascending the chain of the Ghauts, from the Coromandel coast on the east, and descending from it to the level of the sea on the Malabar coast, a distance in all of more than 360 English miles, they found the sum of all the ascents, and of all the descents, reckoned from the level of the sea, to differ from one another only by eight feet and a half. This is the more remarkable, that the angles of elevation and depression, on account of the refraction, are the parts of trigonometrical measurement, in which error is most difficult to be avoided. In every case the angles of elevation and depression between the same objects were constantly measured; and thence the refraction was determined; the double of it being equal to the apparent elevation, plus the horizontal distance in minutes, minus the apparent depression. The refraction seems to have varied from to of the horizontal arc; but as the heights of the barometer and thermometer, at the time