Cosmos: A Sketch of the Physical Description of the Universe, Vol. 1

by Alexander von Humboldt

In the astronomical part of the determination of degrees of latitude, mountain chains, or the denser strata of the Earth, likewise exercise, although in a less degree, an unfavorable influence on the measurement.

As the form of the Earth exerts a powerful influence on the motions of other cosmical bodies, and especially on that of its own neighboring satellite, a more perfect knowledge of the motion of the latter will enable us reciprocally to draw an inference regarding the figure of the Earth. Thus, as Laplace ably remarks,* "An astronomer, without leaving his observatory, may, by a comparison of lunar theory with true observations, not only be enabled to determine the form and size 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."

[footnote] *Laplace, 'Expos. du Syst. du Monde', p. 231.

p 169 The compression which may be inferred from lunar inequalities affords an advantage not yielded by individual measurements of degrees or experiments with the pendulum, since it gives a mean amount which is referable to the whole planet. The comparison of the Earth's compression with the velocity of rotation shows, further, the increase of density from the strata from the surface toward the center — an increase which a comparison of the ratios of the axes of Jupiter and Saturn with their times of rotation likewise shows to exist in these two large planets. Thus the knowledge of the external form of planetary bodies leads us to draw conclusions regarding their internal character.

The northern and southern hemispheres appear to present nearly the same curvature under equal degrees of latitude, but, as has already been observed, pendulum experiments and measurements of degrees yield such different results for individual portions of the Earth's surface that no regular figure can be given which would reconcile all the results hitherto obtained by this method. the true figure of the Earth is to a regular figure as the uneven surfaces of water in motion are on the even surface of water at rest.

When the Earth had been measured, it still had to be weighed. The oscillations of the pendulum* and the plummet have here likewise served to determine the mean density of the Earth, either in connection with astronomical and geodetic operations, with the view of finding the deflection of the plummet from a vertical line in the vicinity of a mountain, or by a comparison of the length of the pendulum in a plain and on the summit of an elevation, or, finally, by the employment of a torsion balance, which may be considered as a horizontally vibrating pendulum for the measurement of the relative density of neighbouring strata.

[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. 563 ('On the Structure of the Internal Parts of the Earth, and the concave habited 'Arch of the Shell'). Halley regarded it as more worthy of the Creator "that the Earth, like a house of several stories, should be inhabited both without and within. For light in the hollow sphere (p. 576) provision might in some manner be contrived."

According to the most recent experiments of Reich, the result obtained is 5.44; that is to say, the mean density of the whole Earth is 5.44 times greater than tht of pure water. As according to the nature of the mineralogical strata constituting the dry continental part of the Earth's surface, the mean density of this portion scarcely amounts to 2.7, and the density of the dry and liquid surface conjointly to scarcely 1.6, it follows that the elliptical unequally compressed layers of the interior must greatly increase in density toward the center, either through pressure or owing to the heterogeneous nature of the substances. Here again we see that the vertical, as well as the horizontally vibrating pendulum, may justly be termed a geognostical instrument.