THE FIGURE AND SIZE OF THE EARTH 1

Abstract

III.DURING the years 1816-52 a Russo-Scandinavian degree-measurement was carried out by Struve and Gen. Tenner, of unusual length and wonderful accuracy. It extended from Hammerfest in the north (70° 40′) to Ismail in the south (45° 20′), a length of 25° 20′. From this it followed that for latitude 56° 3′ 56″, the degree length is 57,137 toises, and in this was included a Swedish degree-measurement which gave 57,209 toises as the length of a degree in lat. 66° 20′ 12″. At this time extensions of earlier operations were undertaken in other countries; as in England with the result of 1/290 for the earth's oblateness. Everest extended Lambton's East Indian degree-measurement, which at present has a length of over twenty-one degrees. Also a longitude measurement begun at an earlier period in Central Europe was recommenced and reaches now from Brest, Paris, Strassburg, Munich, to Vienna. With the assistance of the new data the amount of the earth's oblateness was again investigated, and now that there was no doubt of the accuracy of the measurements, it was shown distinctly that the earth was not an entirely regular elliptical spheroid, that the flattening did not pass regularly over the earth's surface. The theory was next propounded that the earth was an ellipsoid of three axes, but the proposition was not fully supported by the measurements.2 A newly elaborated mathematical method, by which from the existing measurements, the figure of the earth could be obtained, and by which the remaining errors could be reduced to a minimum, was now applied by the great Bessel to the data before him, and according to these principles and on the basis of the best measurements, he obtained dimensions of the earth which still form the ground of all astronomical and geodetical calculations, and which are as follows:—He found for the equatorial radius of the earth 327207714 toises = 6377400 metres; for the polar radius 326113933 toises = 6356080 metres; and for the length of the earth's quadrant 10000855765 metres; while he gave the earth's oblateness as 1/298.153. He also deduced formulæ giving the length of a degree or of a parallel of latitude for any part of the earth; these formulæ will be found in most geodetic handbooks. New values for the dimensions of the earth were, ten years ago, deduced by Leverrier with the assistance of other measurements, but they differ very little from those of Bessel, and in almost all scientific works Bessel's constants are adopted. Thus, about the middle of the present century the solution of the original problem has been attained. And yet since that time there has unmistakably been an altogether unusual progress in all departments concerned in the solution of the problem. First of all, mechanical precision has in the last decades attained such perfection, that now astronomical observations, and especially the geographical determination of places, can be made with considerably greater accuracy than was possible a few decades ago. Moreover, these improvements have been accompanied with extraordinarily suitable new methods. The telegraphic determination of longitude, a method for the determination of the lengths of parallels, has above all, especially in the last ten years, attained such perfection, theoretically and practically, that the measurements carried out on this method are most accurate, and we may justly expect in the future most brilliant results from it. Altogether the problem is near a more substantial solution now than it ever was before, as there are so many well-equipped observatories at work, bound together by a network of the most accurate determination of longitude and latitude, extended over the surface of the earth, and the completion of which is yet going on. Of the greatest importance also in this connection is the more recent theory of measurement, according to which the points to be connected need not lie in one and the same meridian or parallel, but, on the contrary, are connected by an arc of a great circle lying in any direction—the geodetic line.