[footnote] *La Caille's pendulum measurements at the Cape of Good Hope, which have been calculated with much care by Mathieu (Delambre, 'Hist. de l'Astron. au 18me Siecle', p. 479), give a compression of 1/284.4th; but, from several comparisons of observations made in equal latitudes in the two hemispheres (New Holland and the Malouines (Falkland Islands), compared with Barcelona, New York, and Dunkirk), there is as yet no reason for supposing that the mean compression of the southern hemisphere is greater than that of the northern. (Biot, in the 'Mem. de l'Acad. des Sciences', t. viii., 1829, p. 39-41.) Of these three methods* the p 170 last is the most certain, since it is independent of the difficult determination of the density of the mineral masses of which the spherical segment of the mountain consists near which the observations are made. [footnote] *The three methods of observation give the following results: (1.) by the deflection of the plumb-line in the proximity of the Shehallien Mountain (Gaelic, Thichallin) in Perthshire, r.713, as determined by Maskelyne, Hutton, and Playfair (1774-1776 and 1810), according to a method that had been proposed by Newton; (2.) by pendulum vibrations on mountains, 4.837 (Carlini's observations on Mount Cenis compared with Biot's observations at Bordeaux, 'Effemer. Astron. di Milano', 1824, p. 184); (3.) by the torsion balance used by Cavendish, with an apparatus originally devised by Mitchell, 5.48 (according to Hutton's revision of the calculation, 5.32, and according to that of Eduard Schmidt, 5.52; 'Lehrbuch der Math. Geographie', bd. i., s. 487); by the torsion balance, according to Reich, 5.44. In the calculation of these experiments of Professor Reich, which have been made with masterly accuracy, the original mean result was 5.43 (with a probable error of only 0.0233), a result which, being increased by the quantity by which the Earth's centrifugal force diminishes the force of gravity for the latitude of Freiberg (50 degrees 55'), becomes changed to 5.44. The employment of cast iron instead of lead has not presented any sensible difference, or none exceeding the limits of errors of observation, hence disclosing no traces of magnetic influences. (Reich, 'Vrsuche uber die mittlere Dichtigheit der Erde', 1838, s. 60, 62, and 66.) By the assumption of too slight a degree of ellipticity of the Earth, and by the uncertainty of the estimations regarding the density of rocks on its surface, the mean density of the Earth, as deduced from experiments on and near mountains, was found about one sixth smaller than it really is, namely, 4.761 (Laplace, 'Mecan. Celeste', t. v., p. 46), or 4.785. (Eduard Schmidt, 'Lehrb. der Math. Geogr.', bd. i., 387 und 418.) On Halley's hypothesis of the Earth being a hollow sphere (noticed in page 171), which was the germ of Franklin's ideas concerning earthquakes, see 'Philos. Trans.' for the year 1693, vol. xvii., p.