will one day be as perfectly known as the orbit of a planet. In such circumstances, we may congratulate the public, or those, at least, who are interested in the progress of science, on the continuance of the Tri. gonometrical Survey of England, notwithstanding the long and expensive wars in which the country has been engaged since the commencement of it. The expense of the Survey, indeed, is of little moment, compared with the object to be attained by it; but, in all times of difficulty, and in all plans of economy, the indulgences most intellectual and scientific are the first things to be sacrific. ed. It is to the credit of Government that it has been so far otherwise in the present instance. A reflection, naturally called forth by the contemplation of so much accuracy as is displayed in the whole of the work now under our revie., is, how much slower the mathematical arts have advanced than the mathematical sciences. Though the former were no doubt the first to start in the progress of improvement, they appear to have fallen behind, almost from the first outset. The rude manner in which Archimedes measured the apparent diameter of the sun is well known; and while that great geometer was investigating the properties of the sphere and cylinder with an acuteness and depth that have been the admiration of all succeeding ages, he was resolving one of the simplest problems of practical astronomy, in a more inaccurate manner than would be suffered in an ordinary seaman of modern times. When the great problem of measuring the circumference of the earth was first thought of, the principle upon which the solution was attempted was perfectly scientific, and the same, in fact, with that which we have just been considering ; but the execution, though in the hands of able mathematicians, was slovenly and inaccurate in the extreme. The academicians of modern Europe have traversed the globe, from the equator to the polar circlc, in order to resolve this great problem, and are still labouring hard, as we have seen, to give perfect accuracy to their conclusions. The academicians of Greece and Egypt put themselves to no such inconveniency. Eratosthenes, when he engaged in the inquiry, never quitted his observatory, but having measured the sun's solstitial elevation at Alexandria, where he lived, he took for granted, on report, that on the same day the sun was in the zenith of Syené, being seen there from the bottom of a deep well. He also assumed on no better authority, the distance and bearing of the two places, and, with such data, was not ashamed to say that he had computed the circumference of the earth. At a much later period, our countryman Norwood set about determining the circumference a a of the earth, with an accuracy as much superior to that of the Greek geometer, as it was inferior to that which has been the subject of the preceding remarks. Having determined the latitudes of London and York by observation, he travelled from the one place to the other, measuring along the high-road with a chain, and taking the bearings with a compass. He was well satisfied with the accuracy of his work. “ When I measured not," says he, “ I paced ; and I believe the experiment has come within a scantling of the truth.” It is curious to compare these early essays of practical geometry with the perfection to which its operations have now reached, and to consider, that while the artist had made so little progress, the theorist had reached some of the sublimest heights of mathematical speculation ; that the latter had found out the area of the circle, and calculated its circumference to more than a hundred places of decimals, when the former could hardly divide an arch into minutes of a degree; and that many excellent treatises had been written on the properties of curve lines, before a straight line of considerable length, had ever been carefully drawn, or exactly measured, on the surface of the earth. FINIS. |