tice. The former, we suspect, he would not take the trouble to correct, and of the existence of the latter we are not sure that we should easily convince him.

We hope, however, that he will go on, and give us more fragments from his Oriental collections; and, powerful as he is in the expression of the darker passions and more gloomy emotions from which the energy and the terrors of poetry are chiefly derived, we own we should like now and then to meet in his pages with something more cheerful, more amiable, and more tender. The most delightful, and, after all, the most poetical of all illusions are those by which human happiness and human virtue and affection are magnified beyond their natural dimensions, and represented in purer and brighter colours than nature can furnish, even to partial observation. Such enchanting pictures not only gladden life by the glories which they pour on the imagination-but exalt and improve it, by raising the standard both of excellence and enjoyment beyond the vulgar level of sober precept and actual example; and produce on the ages and countries which they adorn, something of the same effect, with the occasional occurrence of great and heroic characters in real life -those moral avatars, by whose successive advents the dignity of our nature is maintained against a long series of degradations, and its divine original and high destination made palpable to the feelings of all to whom it belongs. The sterner and more terrible poetry which is conversant with the guilty and vindictive passions, is not indeed without its use both in purging and in exalting the soul: But the delight which it yields is of a less pure, and more overpowering nature; and the impressions which it leaves behind are of a more dangerous and ambiguous tendency. Energy of character and intensity of emotion are sublime in themselves, and attractive in the highest degree as objects of admiration; but the admiration which they excite, when presented in combination with worthlessness and guilt, is one of the most powerful corrupters and perverters of our moral nature; and is the more to be lamented, as it is most apt to exert its influence on the noblest characters. The poetry of Lord Byron is full of this perversion; and it is because we conceive it capable of producing other and still more delightful sensations than those of admiration, that we wish to see it employed upon subjects less gloomy and revolting than those to which it has hitherto been almost exclusively devoted.

ART. III. An Account of a Trigonometrical Survey, and of the Measurement of an Arc of the Meridian in the Peninsula of India. By Major William Lambton, of the 33d Regiment of Foot.

THE

(From the Asiatic Researches, Vol. VIII. X. & XII.)

HE measurement of the distance between the meridians of Paris and of Greenwich in 1787, formed a new era in the art of Trigonometrical Surveying. The instruments employed in that operation were of such a superior construction, as to afford a measure of many quantities which were before only known from theory to exist. Though it was perfectly understood that the three angles of a triangle on the surface of a sphe rical body like the earth, must necessarily exceed two right angles, yet a quantity so minute as to bear the same proportion to four right angles which the area of the triangle bore to half the superficies of the globe, had eluded the best intruments yet applied to the purposes of practical geometry. It was not till the survey just mentioned, that the new theodolite of RAMSDEN, in the hands of General Roy, and the repeating circle of BORDA, in those of the French mathematicians, were able to measure a quantity, where even fractions of a second must be accurately ascertained. The exquisite division of the former of these instruments, and the power possessed by the latter, of not only measuring any angle, but any multiple of it, and any number of multiples, rendered them perfectly equal to such delicate observations. The advantage of this was quickly perceived; for the spherical excess, or the excess of the three angles of the triangle above two right angles, depending entirely on the area of the triangle, could be estimated with sufficient accuracy before the angles were correctly determined, and therefore might serve for a check on the observations, as effectual as that which is furnished by the well known property of plane triangles, that the three angles are always equal to 180 degrees. This was remarked by General Roy, and applied to the purpose of estimating the accuracy and correcting the errors of his observations. The French geometers carried their views farther; and in seeking to turn the knowledge of this limit to the greatest advantage, LE GENDRE discovered, that if each of the angles of a small spherical triangle be diminished by one third of the spherical excess, their sincs become proportional to the lengths of the opposite sides of the triangle, so that the ratios of the sides may be found by the rules of plane trigonometry.

In a science where all the parts are necessarily connected with

one another, one improvement can seldom fail of leading to many more. It now became evident, that to carry, through the whole process of a trigonometrical survey, the same accuracy that was employed in measuring the angles of the triangles, methods of calculation must be introduced to which it was before quite unnecessary to resort. Thus, if the object was the measurement of an arch of the meridian, the reduction of the. sides of the triangles to the direction of that line, by the usual method of letting fall perpendiculars on it, from the extremities of those sides, and finding the lengths of the parts intercepted, by the rules of plane trigonometry, did not possess a degree of accuracy equal to that which belonged to other parts of the process. The perpendiculars drawn to the meridian from any two points, are not in strictness to be regarded as straight lines, but as arches of two great circles perpendicular to it, which would meet if produced in the pole of the meridian, or in the point of the horizon which is due east or west from the place of observation. It is therefore by the solution of a spherical triangle, of which the sides are nearly quadrants and the base very small, that the reduction required is to be made. This is the method followed by DE LAMBRE in the measurement of the great arch of the meridian carried across France, for the purpose of determining the length of the metre. It is a refinement which was not thought of by General Roy; and we are not sure that it has been followed by any of the geometers who succeeded him in the conduct of the British survey. It is one however which, when the utmost accuracy is aimed at, ought not to be neglected, especially in high latitudes, where the convergency of the meridians is considerable.

Another refinement which one should suppose might be even more easily dispensed with than the former, applies to the measurement of the base from which the sides of the triangles are determined. That line is usually measured by placing rods of equal lengths, or chains stretched with great care, at the ends of one another, for a distance of five or six miles. It has been usual to consider the base, thus measured, as a straight line, the length of which is just equal to the sum of the lengths of all the rods or chains which have been consecutively placed at the ends of one another. The truth however is, that these rods have not been placed exactly in the same straight line, and that they constitute the sides of a polygon inscribed in a circle, the radius of which is the radius of curvature of the earth at the point, and in the direction in which the base is extended. The line measured is therefore, in fact, an arch, passing through the angles of this polygon; and this arch, which is the real base,

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is longer than the sum of the rods or chains. It is, however, easy to see that the deduction of the real length from the apparent, is not, in this case, a matter of much difficulty.

There is another way of including these corrections, which has been thought preferable by some geometers, and is recommended by the authority of DE LAMBRE. According to it, the spherical angles, or those actually measured, are reduced to the angles of the chords; and thus the lengths of the chords are calculated by plane trigonometry, and thence the lengths of the arches themselves are afterwards deduced. The base, measured as above, is also reduced on the chord. This method, though less direct than the former, has considerable advantages in calculation. It was followed by MAJOR LAMBTON in the survey of which we are now to treat.

A third source of inaccuracy, which had never before been thought of, drew the attention both of the French and English mathematicians engaged in the survey. Triangles, as we have seen, on the surface of the earth, cannot be regarded as plane triangles, because the plummets at the three angular points are not parallel to one another, and of course the theodolites at these three stations can neither be in the same, nor in parallel planes. But neither can they always be regarded as spheri cal 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 southermost of the Balearic Isles). Indeed, the book in which the facts and investigations respecting this measurement have been recorded by the French mathematicians, the Base Metrique, 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 improve ments, 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

* They have sent out parties, in all directions, for the purpose of ascertaining the bearings and distances of the places which com. pose 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 meriterious.