154
HISTORY OF PHYSICAL ASTRONOMY.
by means of a simple adjustment he brought it to make the same numberof oscillations in a given time from -whatever point it was suspended.When this took place, it clearly followed that the length of a simple pen-dulum oscillating at the same rate was measured by the distance betweenthe two points of suspension Captain Kater shortly afterwards madeexperiments with the pendulum at various stations of the British arc.He employed a pendulum of a constant length in all his operations, anddetermined the variation of gravity by counting the number of oscillationswhich it made at each station in a mean solar day. A comparison of theresults obtained by him at Unst, in the Shetland Isles , and Dunnose, inthe Isle of Wight, the two extreme stations, gave T for the ellipticityof the earth f. One peculiarity of these experiments consisted in the cor-rection for the altitude of the station being different from that hithertoemployed. Dr. Young had previously remarked that this correction wasin all cases too great, as no account was taken of the attraction of theelevated mass on which the experiments in each instance were made j.If we were raised on a sphere a mile in diameter, and having a densityequal to the mean density of the earth, its attraction would be about -g-g^gtliof the attraction of the whole earth, and the correction for the elevation ofthe station, which would be -jihiTS ^ the attraction varied merely accordingto the inverse square of the distance, would be thereby reduced to or
only about three-fourths of the usual correction. Dr. Young’s researchesinduced him to conclude, that if the mean density of the earth be assumedequal to 5.5, and that of an elevated tract of table land to be 2.5, the truecorrection will be less than that hitherto employed in the ratio of 66 to100. The necessity for a change in the usual correction, on the groundsassigned by the philosopher just cited, cannot admit of any doubt; but thetrue correction, which it will he necessary to apply in each case, will alwaysbe liable to great uncertainty on account of our ignorance of the density ofthe elevated mass, and the exact conformation of its materials. For thesereasons it will generally be the safest mode of proceeding to perform all ex-periments of this kind at inconsiderable altitudes above the level of the sea.
In the year 1817, Captain Freycinet, of the French Navy, was sent outby liis government on a voyage round the world, one of the principal objectsof which was to swing the pendulum in different latitudes. Experimentswere made by him at various stations on each side of the equator, and acomparison of his results gave f° r the ellipticity of the earth §.
His countryman, Captain Duperrey, made a number of similar experimentsin. the course of an expedition of discovery -which he commanded in theyears 1822-25. The ellipticity assigned by a comparison of his resultswas 1|. A great number of valuable experiments with invariable
pendulums were made by Captain Sabine 11 in different parts of the world.He obtained for the ellipticity, as the final result deducible from
them. Experiments with invariable pendulums have also been made byGoldingham* **, at Madras, and, by his directions, at a small island in the
* Phil. Trans. 1818. f Ibid. 1819. i Ibid. 1819.
§ This is the value of the ellipticity which Mr. Baiiy deduced from Freycinet’s obser-vations after applying to them the true correction for the reduction to a vacuum. SeeMem. Ast. Soc ., vol. vii. For an account of Freycinet’s experiments, see Voyage autourdu Monde. Paris , 1825.
II This result is also that of Mr. Baiiy. For an account of Duperrey’s experiments,see the Connaissance des Temps for 1830.
11 Account of experiments for the purpose of determining the Figure of the Earth ,London , 1823.
** Phil. Trans. 1822.