The end of the last century, and the beginning of the present, have been distinguished by a series of Geographical and Astronomical measurements, more accurate and extensive than any yet recorded in the history of science. A proposal made by Cassini in 1783, for connecting the Observatories of Paris and Greenwich by a series of triangles, and for ascertaining the relative position of these two great centres of Astronomical knowledge by actual measurement, gave a beginning to the new operations. The junction of the two Observatories was executed with great skill and accuracy by the geometers of England and France: the new resources displayed, and the improvements introduced, will cause this survey to be remembered as an Era in the practical application of Mathematical science. * From the Edinburgh Review, Vol. XXX. (1818.)-ED. A great revolution had just begun to take place in the construction of instruments intended for the measurement of angles, whether in the heavens or on the surface of the earth; and was much accelerated by the experience acquired in this survey. One part of this improvement consisted in the substitution of the entire circle for the quadrant, the semicircle, or other portions of the same curve, as the unity and simplicity of the entire circle, distinguish it above all figures, and give it no less advantage in Mechanics than in Geometry. Circular instruments admit of being better supported, more accurately balanced, and are less endangered from unequal strain or pressure, than any other. The dilatation and contraction from heat and cold, act uniformly over the whole, and do not change the ratio of the divisions on the circumference. A geometrical property of the same curve contributes also much to the perfection of those instruments, in which the whole circumference is employed ; and though it be quite elementary, and has been long known to geometers, it was first turned to account by artists about the time of which we now speak. The proposition is, that two lines intersecting one another in any point within a circle, cut off opposite arches of the circumference, the sum of which is the same as if they intersected one another in the centre. Hence it follows, that, in a circular instrument, whether the centre about |