nomical measurement of a degree, pendulum experiments, and calculations of the inequalities in the latitude and longitude of the moon. In the application of the first method two separate processes are required, namely, measurements of a degree of latitude on the arc of a meridian, and measurements of a degree of longitude on different parallels.

Although seven years have now passed since I brought forward the results of Bessel's important labours, in reference to the dimensions of our globe, in my General Delineation of Nature, his work has not yet been supplanted by any one of a more comprehensive character, or based upon more recent measurements of a degree. An important addition and great improvements in this department of inquiry may, however, be expected on the completion of the Russian geodetic measurements, which are now nearly finished, and which, as they extend almost from the North Cape to the Black Sea, will afford a good basis of comparison for testing the accuracy of the results of the Indian survey.

According to the determinations published by Bessel in the year 1841, the mean value of the dimensions of our planet was, according to a careful investigation of ten mea

early death has proved a severe loss to science, in Poggendorff's Annalen der Physik und Chemie. Bd. xxxiii, 1834, s. 229–233.

7 The first accurate comparison of a large number of geodetic measurements (including those made in the elevated plateau of Quito, two East Indian measurements, together with the French, English, and recent Lapland observations) was successfully effected by Walbeck, at Abo, in 1819. He found the mean value for the earth's ellipticity to be 302-781, and that of a meridian degree 57009.758 toises, or 324,628 feet. Unfortunately his work, entitled De Forma et Magnitudine Telluris has not been published in a complete form. Excited by the encouragement of Gauss, Eduard Schmidt was led to repeat and correct his results in his admirable Handbook of Mathematical Geography, in which he took into account both the higher powers given for the ellipticity, and the latitudes observed at the intermediate points, as well as the Hanoverian measurements and those which had been extended as far as Formentera by Biot and Arago. The results of this comparison have appeared in three forms, after undergoing a gradual correction, namely, in Gauss's Bestimmung der Breitenunterschiede von Göttingen und Altona 1828, s. 82; in Eduard Schmidt's Lehrbuch der Mathem. und Phys. Geographie, 1829, Th. 1, s. 183, 194-199; and lastly in the preface to the latter work (s. 5). The last result is, for a meridian degree 57008.655 toises, or 324,261 feet; for the ellipticity, 7475 Bessel's first work of 1830 had been immediately preceded by Airy's treatise on the Figurc of the Earth,

surements of degrees, as follows:-The semi-axis major of a rotating spheroid, a form that approximates most closely to

in the Encyclopædia Metropolitana. Ed. of 1849, pp. 220-239. (Here the semi-polar axis was given at 20,853,810 feet-3949.585 miles, the semi-equatorial axis at 20,923,713 feet-3962.824 miles, the meridian quadrant at 32,811,980 feet, and the ellipticity at 2933). The great astronomer of Königsberg was uninterruptedly engaged, from 1836 to 1842, in calculations regarding the figure of the earth, and as his earlier works were emended by subsequent corrections, the admixture of results of investigations at different periods of time has, in many works, proved a source of great confusion. In numbers, which from their very nature are dependent on one another, this admixture is rendered still more confusing from the erroneous reduction of measurements; as, for instance, toises, metres, English feet, and miles of 60 and 69 to the equatorial degree; and this is the more to be regretted since many works, which have cost a very large amount of time and labour, are thus rendered of much less value than they otherwise would be. In the summer of 1837, Bessel published two treatises, one of which was devoted to the consideration of the influence of the irregularity of the earth's figure upon geodetic measurements, and their comparison with astronomical determinations, whilst the other gave the axes of the ob late spheroid, which seemed to correspond most closely to existing measurements of meridian arcs (Schum. Astr. Nachr. bd. xiv, No. 329, s. 269, No. 333, s. 345). The results of his calculation were 3271953.854 toises for the semi-axis major; 3261072.900 toises for the semi-axis minor; and for the length of a mean meridian degree, that is to say, for the ninetieth part of the earth's quadrant (vertically to the equator), 57011.453 toises. An error of 68 toises, or 440.8 feet, which was detected by Puissant, in the mode of calculation that had been adopted, in 1808, by a Commission of the National Institute for determining the distance of the parallels of Montjouy, near Barcelona, and Mola in Formentera, led Bessel, in the year 1841, to submit his previous calculations regarding the dimensions of the earth to a new revision. (Schum. Astr. Nachr. Bd. xix, No. 438, 8. 97-116). This correction yielded for the length of the earth's quadrant 5131179.81 toises, instead of 5130740 toises, which had been obtained in accordance with the first determination of the metre; and for the mean length of a meridian degree, 57013.109 toises, which is about 0.611 of a toise more than a meridian degree, at 45° lat. The numbers given in the text are the result of Bessel's latest calculations. The length of the meridian quadrant, 5131180 toises, with a mean error of 255.63 toises, is therefore=10000856 metres, which would therefore give 40003423 metres, or 21563.92 geographical miles, for the entire circumference of the earth. The difference between the original assumption of the Commission des Poids et Mesures, according to which the metre was the forty-millionth part of the earth's circumference, amounts for the entire circumference to 3423 metres, or 1756.27 toises, which is almost two geographical miles, or more accurately

the irregular figure of our earth, was 3272077.14 toises, or 20,924,774 feet; the semi-axis minor, 3261139.33 toises, or 20,854,821 feet; the length of the earth's quadrant, 5131179.81 toises, or 32,811,799 feet; the length of a mean meridian degree, 57013.109 toises, or 364,596 feet; the length of a parallel degree at 0° latitude, and consequently that of an equatorial degree, 57108.52 toises, or 365,186 feet; the length of a parallel degree at 45°, 40449.371 toises, or 258,657 feet; the ellipticity of the earth, 99.152; and the length of a geographical mile, of which sixty go to an equatorial degree, 951.8 toises, or 6086.5 feet.

The table (page 17) shows the increase of the length of the meridian degree from the equator to the pole, as it has been found from observations, and therefore modified by the local disturbances of attraction

The determination of the figure of the earth by the measurement of degrees of longitude on different parallels requires very great accuracy in fixing the longitudes of different places. Cassini de Thury and Lacaille employed, in 1740, powder signals to determine a perpendicular line at the meridian of Paris. In more recent times, the great trigonometrical survey of England has determined, by the help of far better instruments and with greater accuracy, the lengths of the arcs of parallels and the differences of the meridians between Beachy Head and Dunnose, as well as between Dover and Falmouth. These determinations were, however. only made for differences of longitude of 1°26′ and 6° 22′.8 By far the most considerable of these surveys is the one that was carried on between the meridians of Marennes, on the western coast of France, and Fiume. It extends over the western chain of the Alps, and the plains of Milan and Padua, in a direct distance of 15° 32′ 27′′, and was executed under the direction of Brousseaud and Largeteau, Plana and Carspeaking, 1.84. According to the earliest determinations, the length of the metre was determined at 0.5130740 of a toise, while according to Bessel's last determination it ought to be 0.5131180 of a toise. The difference for the length of the metre is, therefore, 0.038 of a French line. The metre has, therefore, been established by Bessel as equal to 443.334 French lines, instead of 443.296, which is its present legal value (Compare also, on this so-called natural standard, Faye, Leçons de Cosmographie, 1852, p. 93).

8 Airy, Figure of the Earth in the Encycl. Metrop. 1849, pp. 214-216.

lini, almost entirely under the so-called mean parallel of 45°. The numerous pendulum experiments which have been conducted in the neighbourhood of mountain chains, have confirmed in the most remarkable manner the previously-recognised influences of those local attractions which were inferred from the comparison of astronomical latitudes with the results of geodetic measurements.9

In addition to the two secondary methods for the direct measurement of a degree on meridian and parallel arcs, we have still to refer to a purely astronomical determination of the figure of the earth. This is based upon the action which the earth exerts upon the motion of the moon, or in other words upon the inequalities in lunar longitudes and latitudes. Laplace, who was the first to discover the cause of these inequalities, has also taught us their application by ingeniously showing how they afford the great advantage which individual measurements of a degree and pendulum experiments are incapable of yielding, namely, that of showing in one single result the mean figure of the earth.10 We would

9 Biot, Astr. Physique, t. ii, p. 482, and t. iii, p. 482. A very accurate geodetical measurement, which is the more important from its serving as a comparison of the levels of the Mediterranean and Atlantic, has been made on the parallel of the chain of the Pyrenees by Corabœuf, Delcros, and Peytier.

10 Cosmos, vol. i, p. 160. "It is very remarkable that an astronomer without leaving his observatory, may merely by comparing his observations with analytical results, not only be enabled to determine with exactness the size and degree of ellipticity of the earth, but also its distance from the sun and moon-results that otherwise could only be arrived at by long and arduous expeditions to the most remote parts of both hemispheres. The moon may, therefore, by the observation of its movements render appreciable to the higher departments of astronomy, the ellipticity of the earth, as it taught the early astronomers the rotundity of our earth by means of its eclipses" (Laplace, Expos. du Syst. du Monde, p. 230). We have already in Cosmos, vol. iv, pp. 481532, made mention of an almost analogous optical method suggested by Arago, and based upon the observation that the intensity of the ashcoloured light, that is to say the terrestrial light in the moon, might afford us some information in reference to the transparency of our entire atmosphere. Compare also Airy in the Encycl. Metrop. pp. 189, 236, on the determination of the earth's ellipticity by means of the motions of the moon, as well as at pp. 231-235, on the inferences which he draws regarding the figure of the earth from precession and nutation. According to Biot's investigations, the latter determination would only