meridians under the same degree of latitude, this very circumstance speaks
in favor of the exactness of the instruments and the methods employed, and
of the accuracy and the fidelity to nature of these partial results. The
conclusion to be drawn from the increase of forces of attraction (in the
direction from the equator to the poles) with respect to the figure of a
planet is dependent on the distribution of density in its interior. Newton,
from theoretical principles, and perhaps likewise prompted by Cassini's
discovery, previously to 1666, of the compression of Jupiter,* determined,
in his immortal work, 'Philosophiae Naturalis Principia', that the
compression of the Earth, as a homogeneous mass, was 1/230th.
[footnote] *Brewster, 'Life of Sir Isaac Newton', 1831, p. 162. "The
discovery of the spheroidal form of Jupiter by Cassini had probably directed
the attention of Newton to the determination of its cause, and consequently,
to the investigation of the true figure of the Earth." Although Cassini did
not announce the amount of the compression of Jupiter (1/15th) till 1691
('Anciens Memoires de l'Acad. des Sciences', t. ii., p. 108), yet we know
from Lalande ('Astron.', 3me ed., t. iii., p. 335) that Moraldi possessed
some printed sheets of a Latin work, "On the Spots of the Planets,"
commenced by Cassini, from which it was obvious that he was aware of the
compression of Jupiter before the year 1666, and therefore at least
twenty-one years before the publication of Newton's 'Principia'.
Actual mesurements,
p 165
made by the aid of new and more perfect analysis, have, however, shown that
the compression of the poles of the terrestrial spheroid, when the density
of the strata is regarded as increasing toward the center, is very nearly
1/300th.
Three methods have been employed to investigate the curvature of the Earth's
surface, viz., measurements of degrees, oscillations of the pendulum, and
observations of the inequalities in the Moon's orbit. The first is a direct
geometrical and astronomical method, while in the other two we determine
from accurately observed movements the amount of the forces which occasion
those movements, and from these forces we arrive at the cause from whence
they have originated, viz., the compression of our terrestrial spheroid. In
this part of my delineation of nature, contrary to my usual practice, I have
instanced methods because their accuracy affords a striking illustration of
the intimate connection existing among the forms and forces of natural
phenomena, and also because their application has given occasion to
improvements in the exactness of instruments (as those employed in the
measurements of space) in optical and chronological observations; to greater
perfection in the fundamental branches of astronomy and mechanics in respect
to lunar motion and to the resistance experienced by the oscillations of the
pendulum; and to the discovery of new and hitherto untrodden paths of
analysis. With the exception of the investigations of the parallax of
stars, which led to the discovery of aberration and nutation, the history of
science presents no problem in which the object attained -- the knowledge of
the compression and of the irregular form of our planet -- is so far
exceeded in importance by the incidental gain which has accrued, through a
long and weary course of investigation, in the general furtherance and
improvement of the mathematical and astronomical sciences. The comparison
of eleven measurements of degrees (in which are included three
extra-European, namely, the old Peruvian and two East Indian) gives,
according to the most strictly theoretical requirements allowed for by
Bessel,* a compression
p 166
of 1/299th.
[footnote] *According to Bessel's examination of ten measurements of
degrees, in which the error discovered by Poissant in the calculation of the
French measurements is taken into consideration (Schumacher, 'Astron.
Nachr.', 1841, No. 438, s. 116), the semi-axis major of the elliptical
spheroid of revolution to which the irregular figure of the Earth most
closely approximates is 3,272,077.14 toises, or 20,924,774 feet; the
semi-axis minor, 3,261,159,83 toises, or 20,854,821 feet; and the amount of
compression or eccentricity 1/299.152d; the length of a mean degree of the
meridian, 57,013.109 toises, or 364,596 feet, with an error of + 2.8403
toises, or 18.16 feet, whence the length of a geographical mile is 3807.23
toises, or 6086.7 feet. Previous combinations of measurements of degrees
varied between 1/302d and 1/297th; thus Walbeck ('De Forma of Magnitudine
telluris in demensis arcubus Meridiani definiendis', 1819) gives 1/30278th:
Ed. Schmidt ('Lehrbuch der Mathem. und Phys. Geographie', 1829, s. 5) gives
1/20742d, as the mean of seven measures. Respecting the influence of great
differences of longitude on the polar compression, see 'Bibliotheque
Universelle', t. xxxiii., p. 181, and t. xxxv., p. 50: likewise
'Connaissance des Tems', 1829, p. 290. From the lunar inequalities alone,
Laplace ('Exposition du Syst. du Monde', p. 229) found it, by the older
tables of Burg, to be 1/3245th; and subsequently, from the lunar
observations of Burckhardt and Bouvard, he fixed it at 1/299.1th ('Mecanique
Celeste', t. v., p. 13 and 43).
In accordance with this, the polar radius is 10,938 toises (69,944 feet), or
about 11 1/2 miles, shorter than the equatorial radius of our terrestrial
spheroid. The excess at the equator in consequence of the curvature of the
upper surface of the globe amounts, consequently, in the direction of
gravitation, to somewhat more than 4 3/7th times the height of Mont Blanc,
or only 2 1/2 times the probable height of the summit of the Chawalagiri, in
the Himalaya chain. The lunar inequalities (perturbation in the moon's
latitude and longitude) give according to the last investigations of
Laplace, almost the same result for the ellipticity as the measurements of
degrees, viz., 1/299th. The results yielded by the oscillation of the
pendulum give, on the whole, a much greater amount of compression, viz.,
1/288th.*
[footnote] *The oscillations of the pendulum give 1/288.7th as the general
result of Sabine's great expedition (1822 and 1823, from the equator to 80
degrees north latitude); according to Freycinet, 1/286.2d, exclusive of the
experiments instituted at the Isle of France, Guam, and Mowi (Mawi);
according to Forster, 1/289.5th; according to Duperrey, 1/266.4th; and
according to Lutke ('Partie Nautique', 1836, p. 232), 1/270th, calculated
from eleven stations. On the other hand, Mathieu ('Connais. des Temps',
1816, p. 330) fixed the amount at 1/298.2d, from observations made between
Formentera and Dunkirk; and Biot, at 1/304th, from observations between
Formentera and the island of Ust. Compare Baily, 'Report on Pendulum
Experiments', in the 'Memoirs of the Royal Astronomical Society', vol. vii.,
p. 96; also Borenius, in the 'Bulletin de l'Acad. de St. Petersbourg', 1843,
t. i., p. 25. The first proposal to apply the length of the pendulum as a
standard of measure, and to establish the third part of the seconds pendulum
(then supposed to be every where of equal length) as a 'pes horarius', or
general measure, that might be recovered at any age and by all nations, is
to be found in Huygens's 'Horologium Oscillatorium', 1673, Prop. 25. A
similar wish was afterward publicly expressed, in 1742, on a monument
erected at the equator by Bouguer, La Condamine, and Godin. On the
beautiful marble tablet which exists, as yet uninjured, in the old Jesuits'
College at Quito, I have myself read the inscription, 'Penduli simplicis
aequinoctialis unius minuti secundi archetypus, mensurae naturalis exemplar,
utinam universalis!' From an observation made by La Condamine, in his
'Journal du Voyage a l'Equateur', 1751, p. 163, regarding parts of the
inscription that were not filled up, and a slight difference between Bonguer
and himself respecting the numbers, I was led to expect that I should find
considerable discrepancies between the marble tablet and the inscription as
it had been described in Paris; but, after a careful comparison, I merely
found two "ex arca graduum plusquam trium," and the date of 1745 instead of
1742. The latter circumstance is singular, because La Condamine returned to
Europe in November, 1744, Bouguer in June of the same year, and Godin had
left South America in July, 1744. The most necessary and useful amendment
to the numbers on this inscription would have been the astronomical
longitude of Quito. (Humboldt, 'Recueil d'Observ. Astron.', t. ii., p.
319-354.) Nouet's latitudes, engraved on Egyptian monuments, offer a more
recent example of the danger presented by the grave perpetuation of false or
careless results.
Galileo, who first observed when a boy (having, probably, suffered his
thoughts to wander from the service) that the height of the vaulted roof of
a church might be measured by the time of the vibration of the chandeliers
suspended at different altitudes, could hardly have anticipated that the
pendulum would one day be carried from pole to pole, in order to determine
the form of the Earth, or, rather, that the unequal density of the strata of
the Earth affects the length of the seconds pendulum by means of intricate
forces of local attraction, which are, however, almost regular in large
tracts of land. These geognostic relations of an instrument intended for
the measurement of time -- this property of the pendulum, by which, like a
sounding line, it searches unknown depths, and reveals in volcanic islands,*
or in the declivity of elevated continental mountain chains,** dense masses
of basalt and melaphyre instead of cavities, render it difficult,
notwithstanding the admirable simplicity of the method, to arrive at any
great result regarding the figure of the Earth from observation of the
oscillations of the pendulum.
[footnote] *Respecting the augmented intensity of the attraction of
gravitation in volcanic islands (St. Helena, Ualan, Fernando de Noronha,
Isle of France, Guam, Mowe, and Galapagos), Rawak (Lutke, p. 240) being an
exception, probably in consequence of its proximity to the highland of New
Guinea, see Mathieu, in Delambre, 'Hist. de l'Astronomie, au 18me Siecle',
p. 701.
[footnote] **Numerous observations also show great irregularities in the
length of the pendulum in the midst of continents, and which are ascribed to
local attractions. (Delambre, 'Mesure de la Meridienne', t. iii., p. 548;
Biot, in the 'Mem. de l'Academie des Sciences', t. viii., 1829, p. 18 and
23.) In passing over the South of France and Lombardy from west to east, we
find the minimum intensity of gravitation at Bordeaux; from thence it
increases rapidly as we advance eastward, through Figeac, Clermont-Ferrand,
Milan, and Padua; and in the last town we find that the intensity has
attained its maximum. The influence of the southern declivities of the Alps
is not merely t on the general size of their mass, but (much more), in the
opinion of Elie de Beaumont ('Rech. sur les Revol. de la Surface du Globe',
1830, p. 729), on the rocks of melaphyre and serpentine, which have elevated
the chain. On the declivity of Ararat, which with Caucasus may be said to
lie in the center of gravity of the old continent formed by Europe, Asia,
and Africa, the very exact pendulum experiments of Fedorow give indications,
not of subterranean cavities, but of dense volcanic masses. (Parrot, 'Reise
zum Ararat', bd. ii., s. 143.) In the geodesic operations of Carlini and
Plana, in Lombardy, differences ranging from 20" to 47".8 have been found
between direct observations of latitude and the results of these operations.
(See the instances of Andrate and Mondovi, and those of Milan and Padua, in
the 'Operations Geodes. et Astron. pour la Mesure d'un Arc du Parallele
Moyen', t. ii., p. 347; 'Effemeridi Astron. di Milano', 1842, p. 57.) The
latitude of Milan, deduced from that of Berne, according to the , is
45ºdegrees 27' 52", while, according to direct astronomical observations,
it is 45 degrees 27' 35". As the perturbations extend in the plain of
Lombardy to Parma, which is far south of the Po (Plana, 'Operat. Geod.', t.
ii., p. 847), it is probable that there are deflecting causes 'concealed
beneath the soil of the plain itself'. Struve has made similar experiments
[with corresponding results] in the most level parts of eastern Europe.
(Schumacher, 'Astron. Nachrichten', 1830, No. 164, s. 399.) Regarding the
influence of dense masses supposed to lie at a small depth, equal to the
mean height of the Alps, see the analytical expressions given by Hossard and
Rozet, in the 'Comptes Rendus', t. xviii., 1844, p. 292, and compare them
with Poisson, 'Traite de Mecanique' (2me ed., t. i., p. 482. The earliest
observations on the influence which different kinds of rocks exercise on the
vibration of the pendulum are those of Thomas Young, in the 'Philos.
Transactions' for 1819, p. 70-96. In drawing conclusions regarding the
Earth's curvature from the length of the pendulum, we ought not to overlook
the possibility that its crust may have undergone a process of hardening
previously to metallic and dense basaltic masses having penetrated from
great depths, through open clefts, and approached near the surface.
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.
The results obtained by the employment of an instrument of this kind have
led celebrated physicists, according to the difference of the hypothesis
from which they started, to adopt
p 171
entirely opposite views regarding the nature of the interior of the globe.
It has been computed at what depths liquid or even gaseous substances would,
from the pressure of their own superimposed strata, attain a density
exceeding that of platinum or even iridium; and in order that the
compression which has been detrmined within such narrow limits might be
brought into harmony with the assumption of simple and infinitely
compressible matter, Leslie has ingeniously conceived the nucleus of the
world to be a hollow sphere, filled with an assumed "imponderable matter,
having an enormous force of expansion." These venturesome and arbitrary
conjectures have given rise, in wholly unscientific circles, to still more
fantastic notions. The hollow sphere has by degrees been peopled with
plants and animals, and two small subterranean revolving planets -- Pluto
and Proserpine -- were imaginatively supposed to shed over it their mild
light; as, however, it was further imagined that an ever-uniform temperature
reigned in these internal regions, the air, which was made self-luminous by
compression, might well render the planets of this lower world unnecessary.
Near the north pole, at 80 degrees latitude, whence the polar light
emanates, was an enormous opening, through which a descent might be made
into the hollow sphere, and Sir Humphrey Davy and myself were even publicly
and frequently invited by Captain Symmes to enter upon this subterranean
expedition: so powerful is the morbid inclination of men to fill unknown
spaces with shapes of wonder, totally unmindful of the counter evidence
furnished by well-attested facts and universally acknowledged natural laws.
Even the celebrated Halley, at the end of the seventeenth century, hollowed
out the Earth in his magnetic speculations. Men were invited to believe
that a subterranean freely-rotating nucleus occasions by its position the
diurnal and annual changes of magnetic declination. It has thus been
attempted in our own day, with tedious solemnity, to clothe in a scientific
garb the quaintly-devised fiction of the humorous Holbert.*
[footnote] *[The work referred to, one of the wittiest productions of the
learned Norwegian satirist and dramatist Holberg, was written in Latin, and
first appeared under the following title: 'Nicolai Klimii iter subterraneum
novam telluris theoriam ac historiam quintae monarchi Nicolai Klimii iter
subterraneum novam telluris theoriam ac historiam quintae monarchi ad huc
nobis incognitae exhibens e bibliotheca b. Abelini. Hafniae et Lipsiae sunt.
Jac. Preuss', 1741. An admirable Danish translation of this learned but
severe satire on the institutions, morals, and manners of the inhabitants of
the upper Earth, appeared at Copenhagen in 1789, and was entitled 'Niels
Klim's underjordiske reise ocd Ludwig Holberg, oversal after den Latinske
original of Jens Baggesen'. Holberg, who studied for a time at Oxford, was
born at Bergen in 1685, and died in 1754 as Rector of the University of
Copenhagen.] -- Tr.