Figure of the Earth. 147 



thod lias a great advantage over actual measurement, for it is 

 independent of irregularities on the surface of the earth, or or 

 inequalities in its internal constitution. 



Observations upon the length of the pendulum, beating seconds 

 in different latitudes, also furnish a method by which the compres- 

 sion may be determined. Tfye length of the seconds pendulum 

 may be demonstrated to be exactly proportioned to the force of 

 gravity at the place of observation. The comparison of such 

 observations at different latitudes will afford the data for calcu- 

 lating the lengths of the pendulum at the Pole, and beneath the 

 Equator : these being respectively proportioned to the gravitating 

 forces at these places, give the numerator and denominator of a 

 fraction, that subtracted from £ of ^^, furnishes an expression 

 for the oblateness of the generating ellipse in conformity with 

 the theorem of Clairaut. This mode of determining the figure of 

 the earth is better, for several reasons, than that of ascertaining 

 the same fact, from the measure of degrees, whether distant or 

 contiguous. 



It has been shewn by the investigations of Laplace, that the 

 term of the formula in which error may arise from the causes of 

 anomaly, has a coefficient, that is five times as great when the 

 ellipticity is inferred from degrees of the meridian, as it is when 

 it is determined from the lengths of the pendulum in different 

 latitudes. The mode of ascertaining the length of the pendulum 

 vibrating seconds has been of late years so much improved, as to 

 have become a very simple experiment, that may be well per- 

 formed by a single competent observer; while the measure of a 

 degree of the meridian is a laborious, tedious, and expensive 

 process. 



The work, whose title appears at the head of the present 

 article, is for the most part occupied with an account of experi- 

 ments, made to determine the length of the pendulum vibrating 

 seconds in different latitudes, and in both hemispheres. They 

 were performed during two voyages made in public vessels, and 

 in the employ of government : in the first, the author visited and 

 performed experiments at Sierra Leone, St. Thomas', the Island 

 of Ascension, Bahia, Maranham, Trinidad, Jamaica, and New 

 York; during the second, he landed, and experimented, at Ham- 

 merfest, Fairhaven in Spitzbergen, on the coast of Greenland, 

 and at Drontheim. 



The method principally relied upon by our author, and employed 

 by him at all his stations, is the same which was previously used 

 by Captain Kater at the several stations of the British Trigo- 

 nometrical Survey, as detailed by him in the Philosophical Trans- 

 actions for 1819. The fundamental experiment of this method 

 consists in suspending a pendulum alternately, from two knife 



L 2 



