REVIEW OF LAMBTON'S INDIAN SURVEY.* THE 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 mea. sure 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 spherical 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 instruments yet applied to the purposes of practical geometry. It was not till the survey just mentioned, that the new theodolite of Ramsden, in From the Edinburgh Review, Vol. XXI. (1813.)-En. 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, Legendre discovered, that if each of the angles of a small spherical triangle be diminished by onethird of the spherical excess, their sines become proportional to the lengths of the opposite sides of |