the sides. This serves to place the whole in its proper po sition with respect to the cardinal points. The next thing to be done is to place the tract surveyed between the two parallels of latitude on the artificial globe, corresponding to those on the surface of the earth which they represent. This is done by determining by astronomical observations the latitudes of any two stations in the survey at a considerable distance north and south from each other. When this is performed, and the magnitude of the celestial arc in the heavens expressed in degrees is compared with the measured length of the terrestrial meridian between the parallels passing through the stations, the length of a degree on the earth's surface will be known.

The position of the whole as to its distance from the equator or pole will now be known; but its distance east or west from some known meridian, that is, its difference of longitude, remains to be determined. This must be found by means taught in the doctrines of astronomy.

Colonel Lambton, being in possession of some valuable instruments, and in expectation of others from England, which the India Company had with the most laudable liberality given him permission to procure, began the survey by measuring a base on the table-land of the Mysore country, near Bangalore: it was more than 100 miles from the sea, and on this account unfavourable, because its elevation above the level of the sea required to be found, and this could only be done by corresponding observations of the barometer made at the base and at Madras. However, having provided an apparatus similar to that employed for a like purpose in the British survey, he commenced his labour on 14th October, 1800, and completed it on 10th December. After making the necessary corrections for the expansion and contractions of the chain by heat and cold during the process, he found the true length of the base, at the temperature of 62° and reduced to the level of the sea, to be 39,267.706 feet, or 7.4321 miles. By a series of subsequent astronomical observations, the latitude of the south end of the base was found to be 12° 54′ 6′′.

Colonel Lambton resumed his labour in the year 1802. He had by this time received a most complete apparatus from England: this enabled him to execute his views on the scale originally proposed, which was the measurement

of a considerable arc of the meridian. Without regarding what he had formerly done, he began anew, and fixed on a tract of country for a base near Madras. It was well adapted to his purpose, being an entire flat, extending in a southerly direction almost eight miles. The length of the base, reduced to the level of the sea and the temperature 32°, was 40,006.44 feet, or 7.546 miles. The latitude of the north end was 13° 0' 29", and it made an angle of about 12° with the meridian. From this a series of triangles was carried about eighty-five miles westward, extending north to the parallel of 13° 19′ 49", and south to Cuddalore, in latitude 11° 44′ 53′′, embracing an extent of 3700 square miles. The country seems to be favourable to the choice of stations, and the climate to geodetical observations, for the triangles are of considerable magnitude, the sides of some being thirty or forty miles in length. They are also well contrived for avoiding very acute or very obtuse angles, which are unfavourable to accuracy in trigonometrical surveys. In computing the sides, Colonel Lambton reduced the observed spherical angles to the angles of the chords of the arcs, according to the method of Delambre. The chords, which were the sides of the triangles, were then converted into arcs; and as by a very judicious arrangement,—which is, however, not always practicable, he had contrived that the sides of four triangles which connected the stations at the north and south extremities of the meridian should be very nearly in its direction, their sum, with very little deduction, gave the length of the intercepted arc, which was thus found to be 95,721.326 fathoms.

By a series of observations for the latitude at the extremities of this arc, made with an excellent zenith sector of five feet radius by Carey, the amplitude of the corresponding arc in the heavens was found to be 10.58233. The length of the terrestrial arc in fathoms divided by this number gives 60,494 fathoms for the length of a degree in the middle parallel of latitude, viz. 12° 32'. This at the time it was measured was the degree nearest to the equator (except that in Peru almost under it) which had yet been measured, and on that account was highly 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 fifty-five

TRIANGLES CARRIED ACROSS THE PENINSULA. 321

miles, between the stations of Carangooly and Carnaghur, nearly due east and west of one another. To determine the length of this degree, very correct measures of the angles which that line made with the meridians at its extremities were necessary. In fact, the angles were observed with the greatest care; but from the nearness of the intersection of the meridional arc and perpendicular arc to the equator, the result is less to be relied on than the measure of the meridional degree. The degree perpendicular to the meridian of Carangooly was found to be 61,061 fathoms.* By comparing this with the meridional degree, Colonel Lambton found that the earth's compression at the poles should be reckoned 1-210. This, however, we know to be too much; but if we diminish the perpendicular degree by 200 fathoms and make it 60,861, as a writer in the Phil. Trans. 1812 contends that it ought to be because of an error in Colonel Lambton's calculations, then the compression will come out 1-330, which is probably near the truth.

The measurements which we have hitherto described were made in the year 1803. In 1806 the series of triangles was carried quite across the peninsula to the Malabar coast, which they intersected at Mangalore on the north and Tellicherry on the south. They passed over the Ghauts,so celebrated both in the natural and civil history of Hindostan. Two of the stations, Soobramanee and Taddiandamole in the Western Ghauts, not far from the coast, were, the former 5583 feet, and the latter 5682 feet above the level of the sea. The heights of the stations were all determined from the distances and observed angles of elevation; and it is no small proof of their accuracy, that after ascending the chain of the Ghauts from the Coromandel

*The reader should know that the earth is not an exact sphere, but a solid, formed by an ellipse, turning round its lesser axis; so that a meridian is not a circle, but an ellipse, the curvature of which gradually diminishes from the equator to the poles. It is a consequence of this figure that the degrees of latitude gradually increase from the equator to the poles; and the inequality of the degrees in different latitudes depends on the inequality of the axes in such a way that the one is deducible from the other; that is, if we know the proportion which the one axis bears to the other, we can find the proportion which the lengths of degrees in any two parallels, 5° and 10 for example, have to each other, and the contrary. The deviation of the figure of the earth from a perfect sphere is called its compression, and it is measured by the fractional part that the difference of the two axes is of the greater.

coast on the east, and descending again to the level of the sea on the Malabar coast, a distance of more than 360 miles, the sum of all the ascents differed from the sum of the descents only by eight feet and a half.

From the triangles thus carried across the peninsula, a correct measure of its breadth was obtained, and one considerably different from what had previously been supposed. The distance from Madras to the opposite coast was found to be nearly 360 miles, instead of 400 miles as given in the best maps before the time of the survey.

The great extent of the triangulation now required a second base to be measured in the interior of the country. This was accordingly done near Bangalore, about 170 miles west from Madras, not far from the position of the first base. The work was performed with great accuracy by Lieutenant Warren of the 33d regiment. It was connected with the Madras base by the intermediate triangles, and by these its length was computed. The result differed only about three and a half inches from what it was found by the actual measurement,— -a remarkable proof of its accuracy, considering that the two bases were 170 miles distant. Such a near coincidence must produce great confidence in the skill of the observers and the excellence of the instruments they employed. The length of the second base, reduced to the temperature of 62° and to the level of the sea, was 39,793.7 fathoms, or 7.536 miles. The latitudes were determined by the zenith sector with every precaution at both stations; the same stars were observed at both many times, and a mean of the results taken. From the observations it was found that a degree of the meridian in lat. 12° 55′ 10', is 60,498 fathoms.

The next thing attempted was the measurement of a degree perpendicular to the meridian in the above latitude, which is that of Savendroog, near Bangalore; but here an uncertainty similar to that in the former case was found in the result. This, indeed, was inseparable from the nature of the thing to be done. The degree was found to be 60,747.8 fathoms. Colonel Lambton remarks that, supposing the ratio of the earth's diameter to be 1 to 1.003125, the meridional degree 60,498 fathoms gives 60,858 fathoms for the perpendicular degree, which differs by 110 fathoms from what is found by measurement; hence we must infer either

that the earth is not an ellipsoid,* or that this measure is incorrect.

In the year 1810, Colonel Lambton communicated to the Asiatic Society an account of the measurement of an arc on the meridian, extending from lat. 8° 9′ 38′′ to 10° 59′ 49′′ and again, in 1812, he made a further communication on the extension of the meridional arc, from the last-mentioned latitude to 15° 6' 1". His principal object, when he commenced the survey, was to connect the two coasts of Coromandel and Malabar, and to determine the latitudes and longitudes of the principal places, both on the coasts and the interior; but, as the work advanced, his views expanded, and in addition to the triangles carried across the peninsula between the parallels of 12° and 14°, he extended another series from Tranquebar and Negapatam entirely across to Paniani and Calicut; and to render the skeleton complete, a meridional series was carried down the middle of the peninsula, terminating at the sea near Cape Comorin; from this series others were extended to the east and west, entirely along both coasts; so that, in 1812, a web of triangles had been completely woven over the peninsula of India from the parallel of 14° to its southernmost extremity. This triangulation had for its object the determination of the latitudes and longitudes of all the remarkable points; such as tops of mountains, cities, &c. The result of these has been applied to the improvement of the topography of the country; and has been given to the public, we believe, in the excellent maps of that accurate geographer the late Mr. Arrowsmith. The measurements of the meridional arcs, which had a higher aim, the determination of the figure and magnitude of the earth itself, have, however, been most interesting to general geography and astronomy; and, accordingly, Colonel Lambton's various memoirs have found a place in the Asiatic Researches and London Philosophical Transactions, as affording most important data in philosophical and astronomical science.

In the progress of the survey the meridian of the Dodagoontah station, or of Savendroog, was continued south to Punnae, in the lat. of 8° 10'; and the series of triangles for extending its length was continued to the same point.

*Ellipsoid, a solid generated by the revolution of an ellipse about one of its axes: in this case the lesser.