here again refer to the happy expression of the discoverer of this method "that an astronomer without leaving his observatory may discover the individual form of the earth in which he dwells, from the motion of one of the heavenly bodies." After his last revision of the inequalities in the longitude and latitude of our satellite, and by the aid of several thousand observations of Bürg, Bouvard, and Burckhardt," Laplace found by means of his lunar method a compression amounting to, which is very nearly equal to that yielded by the measurements of a degree of latitude

The vibrations of the pendulum yield a third means of determining the figure of the earth (or in other words the relation of the major to the minor axis, on the supposition of our planet being of a spheroidal form), by the elucidation of the law according to which gravity increases from the equator towards the pole. The Arabian astronomers, and more especially Ebn-Junis, at the close of the tenth century, and during the brilliant epoch of the Abbassidian Califs1, first employed these vibrations for the determination of time, and after a neglect of six hundred years the same method was again adopted by Galileo, and Father Riccioli at Bologna.13 The pendulum in conjunction with a system of wheels used to regulate the clocks (which were first employed in the imperfect experiments of Sanctorius at Padua in 1612, and then in the more perfect observations of Huygens in 1656), gave the first material proof of the different intensity of gravity at different latitudes in Richer's comparison of the beats of the same astronomical clock at Paris and Cayenne, in 1672. Picard was indeed engaged in the equipment of this important voyage, but he does not on that account assume to himself the merit of its first suggestion. Richer left Paris

give, for the earth's ellipticity, limiting and widely differing values (4 and 7). Astron. Physique, 3ème éd. t. ii, 1844, p. 463. 11 Laplace, Mécanique Celeste, éd. de 1846, t. v. pp. 16, 53.

12 Cosmos, vol. i, p. 158. Edward Bernard, an Englishman, was the first who recognised the application of the isochronism of pendulum-oscillations in the writings of the Arabian astronomers. (See his letter, dated Oxford, April, 1683, and addressed to Dr. Robert Huntington, in Dublin. Philos. Transac. vol. xii, p. 567.)

13 Fréret de l'Etude de la Philosophie Ancienne in the Mém. de l'Acad. des Inscr. t. xviii (1753), p. 100.

in October, 1671, and Picard in the description of his measurement of a degree of latitude, which appeared in the same year merely refers to " a conjecture which was advanced

14

14 Picard, Mesure de la Terre, 1671, Art. 4. It is scarcely probable that the conjecture which was advanced in the Paris Academy even before the year 1671, to the effect that the intensity of gravity varies with the latitude (Lalande, Astronomie, t. iii, p. 20 § 2668) should have been made by the illustrious Huygens, who had certainly presented his Discours sur la Cause de la Gravité to the Academy in the course of the year 1669. There in no mention made in this treatise of the shortening of the seconds-pendulum, which was being observed by Richer at Cayenne, although a reference to it occurs in the supplements to this work, (one of which must have been completed after the publication of Newton's Principia, and consequently later than 1687). Huygens writes as follows:-" Maxima pars hujus libelli scripta est, cum Lutetiæ degerem (to 1681) ad eum usque locum, ubi de alteratione, quæ pendulis accidit e motu Terræ." See also the explanation which I have given in Cosmos, vol. ii, p. 736. The observations made by Richer at Cayenne were not published until 1679, as I have already observed in the text, and therefore not until fully six years after his return, and what is more remarkable, the annals of the Académie des Inscriptions contain no notice during this long period of Richer's important double observations of the pendulum clock and of the simple seconds-pendulum. We do not know the time when Newton first became acquainted with Richer's results, although his own earliest theoretical speculations regarding the figure of the earth date farther back than the year 1665. It would appear that Newton did not become acquainted until 1682 with Picard's geodetic measurement, which had been published in 1671, and even then "he accidentally heard of it at a meeting of the Royal Society, which he was attending." His knowledge of this fact as Sir David Brewster has shown (Memoirs of Sir I. Newton, vol. i, p. 291), exerted a very important influence on his determination of the earth's diameter, and of the relation which the fall of a body upon our planet bears to the force which retains the moon in its orbit. Newton's views may have been similarly influenced by the knowledge of the spheroidal form of Jupiter which had been ascertained by Cassini prior to 1666, but was first described in 1691 in the Mémoires de l'Académie des Sciences, t. ii, p. 108. Could Newton have learnt anything of a much earlier publication, of which some of the sheets were seen by Lalande in the possession of Maraldi? (Compare Lalande, Astr. t. iii. p. 335, § 3345, with Brewster, Memoirs of Sir I. Newton, vol. i, p. 322, and Cosmos, vol. i, p. 156.) Amid the simultaneous labours of Newton, Huygens, Picard, and Cassini, it is often very difficult to arrive, with any certainty, at a just appreciation of the diffusion of scientific knowledge, owing to the tardiness with which men at that day made known the result of their observations, the publication of which was moreover frequently delayed by accidental cir cumstances.

by one of the members, at a meeting of the Academy, according to which the weight of a body must be less at the equator than at the pole, in consequence of the rotation of the earth." He adds doubtfully, that although it would appear from certain experiments made in London, Lyons, and Bologna, as if the seconds-pendulum must be shortened the nearer we approach to the equator; yet on the other hand he was not sufficiently convinced of the accuracy of the measurements adduced, because at the Hague, notwithstanding its more northern latitude, the pendulum lengths were found to be precisely the same as at Paris. The periods at which Newton first became acquainted with the important pendulum results that had been obtained by Richer as early as 1672, although they were not printed until 1679, and at which he first heard of the discovery that had been made by Cassini, before the year 1666, of the compression of Jupiter's disc, have unfortunately not been recorded with the same exactness, as the fact of his very tardy acquaintance with Picard's measurement of a degree. In an age so remarkable for the successful emulation that distinguished the cultivators of science, and when theoretical views led to the prosecution of observations, which by their results reacted in their turn upon theory, it is of great interest to the history of the mathematical establishment of physical astronomy, that individual epochs should be determined with accuracy.

16

Although direct measurements of meridian and parallel degrees (the former especially in the case of the French measurement of a degree15 between the latitudes 44° 42′ and 47° 30', and the latter by the comparison of points lying to the east and west of the Italian and Maritime Alps)," exhibit great deviations from the mean ellipsoidal figure of the earth, the variations in the amount of ellipticity given by pendulum lengths (taken at different geographical points and in different groups) are very much more striking. The determination of the figure of the earth obtained from the

15 Delambre, Base du Syst. Métrique, t. iii, p. 548.

16 Cosmos, vol. i, p. 159. Plana, Opérations Géodésiques et Astrono miques pour la Mesure d'un Arc du Parallèle Moyen, t. ii, p. 847; Carlini in the Effemeridi Astronomiche di Milano per l'anno 1842,

increase or decrease of gravity (intensity of local attraction), assumes that gravity at the surface of our rotating spheroid must have remained the same as it was at the time of our earth's consolidation from a fluid state, and that no later alterations can have taken place in its density." Notwithstanding the great improvements which have been made in the instruments and methods of measurement by Borda, Kater, and Bessel, there are at present in both hemispheres, from Spitzbergen in 79° 50′ N.L., to the Falkland Islands, in 51° 35′ S.L., where Freycinet, Duperrey, and Sir James Ross successively made their observations, only from 65 to 70 irregularly scattered points,18 at which the length of the simple pendulum has been determined with as much accuracy as the position of the place in respect to its latitude, longitude, and elevation above the level of the sea.

The pendulum experiments made by the French astronomers on the measured part of a meridian arc, and the observations of Captain Kater in the trigonometrical survey of Great Britain concurred, in showing that the results do not individually admit of being referred to a variation of gravity proportional to the square of the sine of the latitude. On this account the English Government determined, at the suggestion of the Vice-President of the Royal Society, Davies Gilbert, to fit out a scientific expedition, which was entrusted to my friend Edward Sabine, who had accompanied Captain Parry on his first polar voyage in the capacity of astronomer. In the course of this voyage, which was continued through the years 1822 and 1823, he coasted along

17 Compare Biot, Astronomie Physique, t. ii, 1844, p. 464, with Cosmos, vol. i, p. 160, and vol. iv, p. 427, where I have considered the difficulties presented by a comparison of the periods of rotation of planets, and their observed compression. Schubert (Astron. Th. iii, s. 316) has also drawn attention to this difficulty, and Bessel in his treatise On Mass and Weight says expressly, that the supposition of the invariability of gravity at any one point of observation has been rendered somewhat uncertain by the recent experiments made on the slow upheaval of large portions of the earth's surface.

18 Airy in his admirable treatise on the Figure of the Earth (Encycl. Metropol. 1849, p. 229) reckoned fifty different stations where trustworthy results had been obtained up to the year 1830, and fourteen others, (those of Bouguer, Legentil, Lacaille, Maupertuis and La Croyère), which however do not bear comparison with the former in point of accuracy.

the western shores of Africa, from Sierra Leone to the Island of St. Thomas, near the Equator, then by Ascension to South America, from Bahia to the mouth of the Orinoco, on his way to the West Indies and the New England States, after which he penetrated into the Arctic regions as far as Spitzbergen, and a hitherto unexplored and ice-bound portion of East Greenland (74° 32'). This brilliant and ably conducted expedition had the advantage of being mainly directed to one sole object of investigation, and of embracing points which are separated from one another by 93° of latitude.

The field of observation in the French expedition for the measurements of degrees was more remote from the equinoctial and arctic zones; but it had the great advantage of presenting a linear series of points of observation, and of affording direct means of comparison with the partial curvature of the arcs obtained by geodetico-astronomical observations. Biot, in 1824, carried the line of pendulum measurements from Formentera (38° 39′ 56") where he had already made observations conjointly with Arago and Chaix, as far as Unst, the most northerly of the Shetland Islands (60° 45′ 25"), and with Mathieu he extended it to the parallels of Bordeaux, Figeac, and Padua, as far as Fiume.19 These pendulum results, when compared with those of Sabine, certainly give for the compression of the whole northern quadrant, but when separated into two halves, they yield a still more varying result, giving from the equator to 45°, and from 45° to the pole.20 It has been shown

19 Biot and Arago, Recueil d'Observ. Géodesiques et Astronomiques, 1821, pp. 526-540, and Biot, Traité d'Astr. Physique, t. ii, 1844, pp. 465473.

20 Op. cit. p. 488. Sabine (Exper. for determining the variation in the length of the Pendulum vibrating Seconds, 1825, p. 352) finds 3.3 from all the thirteen stations of his pendulum expedition, notwithstanding their great distances from one another in the northern hemisphere; and from these, increased by all the pendulum stations of the British survey and of the French geodetic measurement from Formentera to Dunkirk, comprising therefore in all a comparison of twenty-five points of observation he again found.. It is still more striking, as was already observed by Admiral Lütke, that far to the west of the Atlantic region in the meridians of Petropawlowski and New Archangel, the pendulum lengths yield a much greater ellipticity, namely 7. As the previously applied theory of the influence of the air surrounding the pendulum