[footnote] *Plato, 'Phaedo', p. 97. (Arist., 'Metaph.', p. 985.) compare Hegel, 'Philosophie der Geschichte', 1840, s. 16.

The delineation of the principal characteristics of telluric phenomena must begin with the form of our planet and its relations in space. Here too, we may say that it is not only the mineralogical character of rocks, whether they are crystalline, granular, or densely fossiliferous, but the geometrical form of the Earth itself, which indicates the mode of its origin, and is, in fact, its history. An elliptical spheroid of revolution gives evidence of having once been a soft or fluid mass. Thus the Earth's compression constitutes one of the most ancient geognostic events, as every attentive reader of the book of nature can easily discern; and an analogous fact is presented in the case of the Moon, the perpetual direction of whose axes toward the Earth, that is to say, the increased accumulation of matter on that half of the Moon which is turned toward us, determines the relations of the periods of rotation and revolution, and is probably contemporaneous with the earliest epoch in the formative history of this satellite. The mathematical figure of the Earth is that which it would have were its surface covered entirely by water in a state of rest; and it is this assumed form to which all geodesical measurements of degrees refer. This mathematical surface is different from that true physical surface which is affected by all the accidents and inequalities of the solid parts.*

[footnote] *Bessel, 'Allgemeine Betrachtungen uber Gradmessungen nach astronomisch-geodätischen Arbeiten', at the conclusion of Bessel and Baeyer, 'Gradmessung in Ostpreussen', s. 427. Regarding the accumulation of matter on the side of the Moon turned toward us (a subject noticed in an earlier part of the text), see Laplace, 'Expos. du Syst. du Monde', p. 308.

The whole figure of the Earth is determined when we know the amount of the p 164 compression at the poles and the equatorial diameter; in order, however, to obtain a perfect representation of its form it is necessary to have measurements in two directions, perpendicular to one another.

Eleven measurements of degrees (or determinations of the curvature of the
Earth's surface in different parts), of which nine only belong to the
present century, have made us acquainted with the size of our globe, which
Pliny names "a point in the immeasurable universe."*

[footnote] *Plin., ii., 68. Seneca, 'Nat. Quaest., Praef., c. ii. "El mundo espoco" (the Earth is small and narrow), writes Columbus from Jamaica to Queen Isabella on the 7th of July, 1503: not because he entertained the philosophic views of the aforesaid Romans, but because it appeared advantageous to him to maintain that the journey from Spain was not long, if, as he observes, "we seek the east from the west." Compare my 'Examen Crit. de l'Hist. de la Geogr. du 15 me Siecle', t.i., p. 83, and t. ii., p. 327, where I have shown that the opinion maintained by Delisle, Freret, and Gosselin, that the excessive differences in the statements regarding the Earth's circumference, found in the writings of the Greeks, are only apparent, and dependent on different values being attached to the stadia, was put forward as early as 1495 by Jaime Ferrer, in a proposition regarding the determination of the line of demarkation of the papal dominions.

If these measurements do not always accord in the curvatures of different 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.

p 172 The figure of the Earth and the amount of solidification (density) which it has acquired are intimately connected with the forces by which it is animated, in so far, at least, as they have been excited or awakened from without, through its planetry position with reference to a luminous central body. Compression, when considered as a consequence of centrifugal force acting on a rotating mass, explains the earlier condition of fluidity of our planet. During the solidification of this fluid, which is commonly conjectured to have been gaseous and primordially heated to a very high temperature, an enormous quantity of latent heat must have been liberated. If the process of solidification began as Fourier conjectures, by radiation from the cooling surface exposed to the atmosphere, the particles near the center would have continued fluid and hot. As, after long emanation of heat from the center toward the exterior, a stable condition of the temperature of the Earth would at length be established, it has been assumed that with increasing depth the subterranean heat likewise uninterruptedly increases. The heat of the water which flows from deep borings (Artesian wells), direct experiments regarding the temperature of rocks in mines, but, above all, the volcanic activity of the Earth, shown by the flow of molten masses from open fissures, afford unquestionable evidence of this increase for very considerable depths from the upper strata. According to conclusions based certainly upon mere analogies, this increase is probably much greater toward the center.

That which has been learned by an ingenious analytic calculation, expressly perfected for this class of investigations,* p 173 regarding the motion of heat in homogeneous metallic spheroids, must be applied with much caution to the actual character of our planet, considering our present imperfect knowledge of the substances of which the Earth is composed, the difference in the capacity of heat and in the conducting power of different superimposed masses, and the chemical changes experienced by solid and liquid masses from any enormous compression.

[footnote] *Here we must notice the admirable analytical labors of Fourier, Biot, Laplace, Poisson, Duhamel, and Lame. In his 'Theorie Mathematique de la Chaleur', 1835, p. 3, 428-430, 436, and 521-524 (see, also, De la Rive's abstract in the 'Bibliotheque Universelle de Geneve', Poisson has developed an hypothesis totally different from Fourier's view ('Theorie Analytique de la Chaleur'.) He denies the present fluid state of the Earth's center; he believes that "in cooling by radiation to the medium surrounding the Earth, the parts which were first solidified sunk, and that by a double descending and ascending current, the great inequality was lessened which would have taken place in a solid body cooling from the surface." It seems more probable to this great geometer that the solidification began in the parts lying nearest to the center: "the phenomenon of the increase of heat with the depth does not extend to the whole mass of the Earth, and is merely a consequence of the motion of our planetary system in space, of which some parts are of a very different temperature from others, in consequence of stellar heat (chaleur stellaire)." Thus, according to Poisson, the warmth of the water of our Artesian wells is merely that which has penetrated into the Earth from without; and the Earth itself "might be regarded as in the same circumstances as a mass of rock conveyed from the equator to the pole in so short a time as not to have entirely cooled. The increase of temperature in such a block would not extend to the central strata." The physical doubts which have reasonably been entertained against this extraordinary cosmical view (which attributes to the regions of space that which probably is more dependent on the first transition of matter condensing from the gaseo-fluid into the solid state) will be found collected in Poggendorf's 'Annalen', bd. xxxix., s 93-100.

It is with the greatest difficulty that our powers of comprehension can conceive the boundary line which divides the fluid mass of the interior from the hardened mineral masses of the external surface, or the gradual increase of the solid strata, and the condition of semi-fluidity of the earthy substances, these being conditions to which known laws of hydraulics can only apply under considerable modifications. The Sun and Moon, which cause the sea to ebb and flow, most probably also affect these subterranean depths. We may suppose that the periodic elevations and depressions of the molten mass under the already solidified strata must have caused inequalities in the vaulted surface from the force of pressure. The amount and action of such oscillations must, however, be small; and if the relative position of the attracting cosmical bodies may here also excite "spring tides," it is certainly not to these, but to more powerful internal forces, that we must ascribe the movements that shake the Earth's surface. There are groups of phenomena to whose existence it is necessary to draw attention, in order to indicate the universality of the influence of the attraction of the Sun and Moon on the external and internal conditions of the Earth, however little we may be able to determine the quantity of this influence.

According to tolerably accordant experiments in Artesian wells, it has been shown that the heat increases on an average about 1 degree for every 54.5 feet. If this increase can be reduced p 174 to arithmetical relations, it will follow, as I have already observed,* that a stratum of granite would be in a state of fusion at a depth of nearly twenty-one geographical miles, or between four and five times the elevation of the highest summit of the Hinalaya.

[footnote] *See the Introduction. This increase of temperature has been found in the Puits de Grenelle, at Paris, at 58.3 feet; in the boring at the new salt-works at Minden, almost 53.6; at Pregny, near Geneva, according to Auguste de la Rive and Marcet, notwithstanding that the mouth of the boring is 1609 feet above the level of the sea, it is also 53.6 feet. This coincidence between the results of a method first proposed by Arago in the year 1821 ('Annuaire du Bureau des Longitudes', 1835, p. 234), for three different mines, of the absolute depths of 1794, 2231, and 725 feet respectively, is remarkable. The two points on the Earth, lying at a small vertical distance from each other, whose annual mean temperatures are most accurately known, are probably at the spot on which the Paris Observatory stands, and the Caves de l'Observatoire beneath it; the mean temperature of the former is 51.5ºdegrees, and of the latter 53.3ºdegrees, the difference being 1.8ºdegrees for 92 feet, or 1 degree for 51.77 feet. (Poisson, 'Theorie Math. de la Chaleur', p. 415 and 462.) In the course of the last seventeen years, from causes not yet perfectly understood, but probably not connected with the actual temperature of the caves, the thermometer standing there has risen very nearly 0.4 degrees. Although in Artesian wells there are sometimes slight errors from the lateral permeation of water, these errors are less injurious to the accuracy of conclusions than those resulting from currents of cold air, which are almost always present in mines. The general result of Reich's great work on the temperature of the mines in the Saxony mining districts gives a somewhat slower increase of the terrestrial heat, or 1 degree to 76.3 feet. (Reich, 'Beob. uber die Temperatur des Gesteins in verschielen en Tiefen', 1834, s. 134.) Phillips, however, found (Pogg., 'Annalen', bd. xxxiv., s. 191), in a shaft of the coal-mine of Monk-wearmouth, near Newcastle, in which, as I have already remarked, excavations are going on at a depth of about 1500 feet below the level of the sea, an increase of 1 degree to 59.06 feet, a result almost identical with that found by Arago in the Puits de Grenell.

We must distinguish in our globe three different modes for the transmission of heat. The first is periodic, and affects the temperature of the terrestrial strata according as the heat penetrates from above downward or from below upward, being influenced by the different positions of the Sun and the seasons of the year. The second is likewise an effect of the Sun, although extremely slow: a portion of the heat that has penetrated into the equatorial regions moves in the interior of the globe toward the poles, where it escapes into the atmosphere and the remoter regions of space. The third mode of transmission is the slowest of all, and is derived from the secular cooling of the globe, and from the small portion of the primitive heat which is still being disengaged from the surface. p 175 This loss experienced by the central heat must have been very considerable in the earliest epochs of the Earth's revolutions, but within historical periods it has hardly been appreciable by our instruments. The surface of the Earth is therefore situated between the glowing heat of the inferior strata and the universal regions of space, whose temperature is probably below the freezing-point of mercury.

The periodic changes of temperature which have been occasioned on the Earth's surface by the Sun's position and by meteorological processes, are continued in its interior, although to a very inconsiderable depth. The slow conducting power of the ground diminishes this loss of heat in the winter, and is very favorable to deep-rooted trees. Points that lie at very different depths on the same vertical line attain the maximum and minimum of the imparted temperature at very different periods of time. The further they are removed from the surface, the smaller is this difference between the extremes. In the latitudes of our temperate zone (between 48 degrees and 52 degrees), the stratum of invariable temperature is at a depth of from 59 to 64 feet, and at half that depth the oscillations of the thermometer, from the influence of the seasons, scarcely amount to half a degree. In tropical climates this invariable stratum is only one foot below the surface, and this fact has been ingeniously made use of by Boussingault to obtain a convenient, and as he believes, certain determination of the mean temperature of the air of different places.*

[footnote] *Boussingault, 'Sur la Profondeus a laquelle se trouve la Couche de Temperature invariable, entre les Tropiques', in the 'Annales de Chimie et de Physique', t. liii., 1833, p. 225-247.

This mean temperature of the air at a fixed point, or at a group of contiguous points on the surface, is to a certain degree the fundamental element of the climate and agricultural relations of a district; but the mean temperature of the whole surface is very different from that of the globe itself. The questions so often agitated, whether the mean temperature has experienced any considerable differences in the course of centuries, whether the climate of a country has deteriorated, and whether the winters have not become milder and the summers cooler, can only be answered by means of the thermometer; this instrument has, however, scarcely been invented more than two centuries and a half, and its scientific application hardly dates back 120 years. The nature and novelty of the means interpose, therefore, very narrow limits to our investigation regarding the temperature p 176 of the air. It is quite otherwise, however, with the solution of the great problem of the internal heat of the whole Earth. As we may judge of uniformity of temperature from the unaltered time of vibration of a pendulum, so we may also learn, from the unaltered rotatory velocity of the Earth, the amount of stability in the mean temperature of our globe. This insight into the relations between the 'length of the day' and the 'heat of the Earth' is the result of one of the most brilliant applications of the knowledge we had long possessed of the planet. The rotatory velocity of the Earth depends on its volume; and since, by the gradual cooling of the mass by radiation, the axis of rotation would become shorter, the rotatory velocity would necessarily increase, and the length of the day diminish, with a decrease of the temperature. From the comparison of the secular inequalities in the motions of the Moon with the eclipses observed in ancient times, it follows that, since the time of Hipparchus, that is, for full 2000 years, the length of the day has certainly not diminished by the hundredth part of a second. The decrease of the mean heat of the globe during a period of 2000 years has not, therefore, taking the extremest limits, diminished as much as 1/306th of a degree of Fahrenheit.*

[footnote] *Laplace, 'Exp. du Syst. du Monde', p. 229 and 263; 'Mecanique Celeste', t. v., p. 18 and 72. It should be remarked that the fraction 1/306th of a degree of Fahrenheit of the mercurial thermometer, given in the text as the limit of the stability of the Earth's temperature since the days of Hipparchus, rests on the assumption that the dilation of the substances of which the Earth is composed is equal to that of glass, that is to say, 1/18,000th for 1 degree. Regarding this hypothesis, see Arago in the 'Annuaire' for 1834, p. 177-190.

This invariability of form presupposes also a great invariability in the distribution of relations of density in the interior of the globe. The translatory movements, which occasion the eruptions of our present volcanoes and of ferruginous lava, and the filling up of previously empty fissures and cavities with dense masses of stone, are consequently only to be regarded as slight superficial phenomena affecting merely one portion of the Earth's crust, which, from their smallness when compared to the Earth's radius, become wholly insignificant.

I have described the internal heat of our planet, both with reference to its cause and distribution, almost solely from the results of Fourier's admirable investigations. Poisson doubts the fact of the uninterrupted increase of the Earth's heat p 177 from the surface to the center, and is of opinion that all heat has penetrated from without inward, and that the temperature of the globe depends upon the very high or very low temperature of the regions of space through which the solar temperature of the regions of space, through which the solar system has moved. This hypothesis, imagined by one of the most acute mathematicians of our time, has not satisfied physicists or geologists, or scarcely indeed any one besides its author. But, whatever may be the cause of the internal heat of our planet, and of its limited or unlimited increase in deep strata, it leads us, in this general sketch of nature, through the intimate connection of all primitive phenomena of matter, and through the common bond by which molecular forces are united, into the mysterious domain of magnetism. Changes of temperature call forth magnetic and electric currents. Terrestrial magnetism, whose main character, expressed in the three-fold manifestation of its forces, is incessant periodic variability, is ascribed either to the heated mass of the Earth itself,* or to those galvanic currents which we consider as electricity in motion, that is, electricity moving in a closed circuit.**

[footnote] *William Gilbert, of Colchester, whom Galileo pronounced "great to a degree that might be envied," said "magnus magnes ipse est globus terrestris." He ridicules the magnetic mountains of Frascatori, the great contemporary of Columbus, as being magnetic poles: "rejicienda est vulgaris opinio de montibus magneticis, aut rupe aliqua magnetica, aut polo phantastico a polo mundi distante." He assumes the declination of the magnetic needle at any give point on the surface of the Earth to be invariable (variatio uniuscujusque loci constans est), and refers the curvatures of the isogonic lines to the configuration of continents and the relative positions of sea basins, which possess a weaker magnetic force than the solid masses rising above the ocean. (Gilbert, 'de Magnete', ed. 1633, p. 42, 98, 152 and 155.)

[footnote] ** Gauss, 'Allgemcine Theorie des Erdmagnetismus', in the 'Resultate aux den Beob. des Magnet. Vereins', 1838, s. 41, p. 56.

The mysterious course of the magnetic needle is equally affected by time and space, by the sun's course, and by changes of place on the Earth's surface. Between the tropics, the hour of the day may be known by the direction of the needle as well as by the oscillations of the barometer. It is affected instantly, but only transiently, by the distant northern light as it shoots from the pole, flashing in beams of colored light across the heavens. When the uniform horary motion of the needle is disturbed by a magnetic storm, the perturbation manifests itself 'simultaneously', in the strictest sense of the word, over hundreds and thousands of miles of sea and land, or propagates itself by degrees, in short intervals of time, in p 178 every direction over the Earth's surface.*

[footnote] *There are also perturbations which are of a local character, and do not extend themselves far, and are probably less deep-seated. Some years ago I described a rare instance of this kind, in which an extraordinary disturbance was felt in the mines at Freiberg, but was not perceptible at Berlin. ('Lettre de M. de Humboldt a Son Altesse Royale le Duc de Sussex sur les moyens propres a perfectionner la Connaissance du Magnetisme Terrestre', in Becquerel's 'Traite Experimental de l'Electricite' t. vii., p. 442.) Magnetic storms which were simultaneously felt from Sicily to Upsala, did not extend from Upsala to Alten. (Gauss and Weber, 'Resultate des Magnet. Vereins', 1839, 128; Lloyd, in the 'Comptes Rendus de l'Acad. des Sciences', t. xii., 1843, Sem. ii., p. 725 and 827.) Among the numerous examples that have been recently observed, of perturbations occurring simultaneously and extending over wide portions of the Earth's surface, and which are collected in Sabine's important work ('Observ. on Days of unusual Magnetic Disturbance', 1843), one of the most remarkable is that of the 25th of September, 1841, which was observed at Toronto in Canada, at the Cape of Good Hope, at Prague, and partially in Van Diemen's Land. The English Sunday, on which it is deemed sinful, after midnight on Saturday, to register an observation, and to follow out the great phenomena of creation in their perfect development, interrupted the observations in Van Diemen's Land, where in consequence of the difference of the longitude, the magnetic storm fell on the Sunday. ('Observ.', p. xiv., 78, 85, and 87.)

In the former case, the simultaneous manifestation of the storm may serve, within certain limitations, like Jupiter's satellites, fire-signals, and well-observed falls of shooting stars, for the geographical determination of degrees of longitude. We here recognize with astonishment that the perturbations of two small magnetic needles, even if suspended at great depths below the surface, can measure the distances apart at which they are placed, teaching us, for instance, how far Kasan is situated east of Gottingen or of the banks of the Seine. There are also districts in the earth where the mariner, who has been enveloped for many days in mist, without seeing either the sun or stars, and deprived of all means of determining the time, may know with certainty, from the variations in the inclination of the magnetic needle, whether he is at the north or the south of the port he is desirous of entering.*

[footnote] *I have described, in Lametherie's 'Journal de Physique', 1804, t. lix., p. 449, the application (alluded to in the text) of the magnetic inclination to the determination of latitude along a coast running north and south, and which, like that of Chili and Peru, is for a part of the year enveloped in mist ('garua'). In the locality I have just mentioned, this application is of the greater importance, because, in consequence of the strong current running northward as far as to Cape Parena, navigators incur a great loss of time if they approach the coast to the north of the haven they are seeking. In the South Sea, from Callao de Lima harbor to Truxillo, which differ from each other in latitude by 3 degrees 57' I have observed a variation of the magnetic inclination amounting to 9 degrees (centesimal division); and from Callao to Guayaquil, which differ in latitude by 9 degrees 50', a variation of 23.5 degrees. (See my 'Relat. Hist.', t. iii., p. 622.) At Guarmey (10 degrees 4' south lat.), Huaura (11 degrees 3' south lat.), and Chancay (11 degrees 4' south lat.), Huaura (11 degrees 3' south lat.), and Chancay (11 degrees 32' south lat.), the inclinations are 6.80 degrees, 9 degrees, and 10.35 degrees of the centesimal division. The determination of position by means of the magnetic inclination has this remarkable feature connected with it, that where the ship's course cuts the isoclinalline almost perpendicularly, it is the only one that is independent of all determination of time, and consequently, of observations of the sun or stars. It is only lately that I discovered, for the first time, that as early as at the close of the sixteenth century, and consequently hardly twenty years after Robert Norman had invented the inclinatorium, William Gilbert, in his great work, 'De Magnete', proposed to determine the latitude by the inclination of the magnetic needle. Gilbert ('Physiologia Nova de Magnete', lib. v., cap. 8, p. 200) commends the method as applicable "aëre caliginoso." Edward Wright, in the introduction which he added to his master's great work, describes this proposal as "worth much gold." As he fell into the same error with Gilbert, of presuming that the isoclinal lines coincided with the geographical parallel circles, and that the magnetic and geographical equators were identical, he did not perceive that the proposed method had only a local and very limited application.

p 179 When the needle, by its sudden disturbance in its horary course, indicates the presence of a magnetic storm, we are still unfortunately ignorant whether the seat of the disturbing cause is to be sought in the Earth itself or in the upper regions of the atmosphere. If we regard the Earth as a true magnet, we are obliged, according to the views entertained by Friedrich Gauss (the acute propounder of a generaltheory of terrestrial magnetism), to ascribe to every portion of the globe measuring one eighth of a cubic meter (or 3 7/10ths of a French cubic foot) in volume, an average amount of magnetism equal to that contained in a magnetic rod of 1 lb. weight.*

[footnote[ *Gauss and Weber, 'Resultate des Magnet. Vereins', 1838, 31, s. 146.

If iron and nickel, and probably, also, cobalt (but not chrome, as has long been believed),* are the only substances which become permanently magnetic, and retain polarity from a certain coerceive force, the phenomena of Arago's magnetism of rotation and of Faraday's induced currents show, on the other hand, that all telluric substances may possibly be made transitorily magnetic.

According to Faraday ('London and Edinburgh Philosophical Magazine', 1836, vol. viii., p. 178), pure cobalt is totally devoid of magnetic power. I know, however, that other celebrated chemists (Heinrich Rose and Wohler) do not admit this as absolutely certain. If out of two carefully-purified masses of cobalt totally free from nickel, one appears altogether non-magnetic (in a state of equilibrium), I think it probable that the other owes its magnetic property to a want of purity; and this opinion coincides with Faraday's view.

According to the experiments of the p 180 first-mentioned of these great physicists, water, ice, glass, and carbon affect the vibrations of the needle entirely in the same manner as mercury in the rotation experiments.*

[footnote] *Arago, in the 'Annales de Chimie', t. xxxii., p. 214; Brewster, 'Treaties on Magnetism', 1837, p. 111; Baumgartner, in the 'Zeitschrift fur Phys. und Mathem.', bd. ii., s. 419.

Almost all substances show themselves to be, in a certain degree, magnetic when they are conductors, that is to say, when a current of electricity is passing through them.

Although the knowledge of the attracting power of native iron magnets or loadstones appears to be of very ancient date among the nations of the West, there is strong historical evidence in proof of the striking fact that the knowledge of the directive power of a magnetic needle and of its relation to terrestrial magnetism was peculiar to the Chinese, a people living in the extremest eastern portions of Asia. More than a thousand years before our era, in the obscure age of Codrus, and about the time of the return of the Heraclidae to the Peloponnesus, the Chinese had already magnetic carriages, on which the movable arm of the figure of a man continually pointed to the south, as a guide by which to find the way across the boundless grass plains of Tartary; nay, even in the third century of our era, therefore at least 700 years before the use of the mariner's compass in European seas, Chinese vessels navigated the Indian Ocean* under the direction of magnetic needles pointing to the south.

[footnote] *Humboldt, 'Examen Critique de l'Hist. de la Geographie', t. iii., p. 36.

I have shown, in another work, what advantages this means of topographical direction, and the early knowledge and application of the magnetic needle gave the Chinese geographers over the Greeks and Romans, to whom, for instance, even the true direction of the Apennines and Pyrenees always remained unknown.*

[footnote] *'Asie Centrale', t. i., Introduction, p. xxxviii-xlii. The Western nations, the Greeks and the Romans, knew that magnetism could be communicated to iron, 'and that that metal would retain it for a length of time'. ("Sola haec materia ferri vires, a maguete lapide accipit, 'retinetque longo tempore." Plin., xxxiv., 14.) The great discovery of the terrestrial directive force depended, therefore, alone on this, that no one in the West had happened to observe an elongated fragment of magnetic iron stone, or a magnetic iron rod, floating, by the aid of a piece of wood, in water, or suspended in the air by a thread, in such a position as to admit of free motion.

The magnetic power of our globe is manifested on the terrestrial surface in three classes of phenomena, one of which exhibits itself in the varying intensity of the force, and the two others in the varying direction of the inclination, and in p 181 the horizontal deviation from the terrestrial meridian of the spot. Their combined action may therefore be graphically represented by three systems of lines, the 'isodynamic, isoclinic', and 'isogonic' (or those of equal force, equal inclination, and equal declination). The distances apart, and the relative positions of these moving, oscillating, and advancing curves, do not always remain the same. The total deviation (variation or declination of the magnetic needle) has not at all changed, or, at any rate, not in any appreciable degree, during a whole century, at any particular point on the Earth's surface,* as, for instance, the western part of the Antilles, or Spitzbergen.

[footnote] *A very slow secular progression, or a local invariability of the magnetic declination, prevents the confusion which might arise from terrestrial influences in the boundaries of land, when, with an utter disregard for the correction of declination, estates are, after long intervals, measured by the mere application of the compass. "The whole mass of the bottomless pit of endless litigation by the invariability of the magnetic declination in Jamica and the surrounding Archipelago during the whole of the last century, all surveys of property there having been conducted solely by the compass." See Robertson in the 'Philosophical Transactions' for 1806, Part ii., p. 348, 'On the Permanency of the Compass in Jamaica since 1660'. In the mother country (England) the magnetic declination has varied by fully 14 degrees during the period.

In like manner, we observe that the isogonic curves, when they pass in their secular motion from the surface of the sea to a continent or an island of considerable extent, continue for a long time in the same position, and become inflected as they advance.

These gradual changes in the forms assumed by the lines in their translatory motions, and which so unequally modify the amount of eastern and western declination, in the course of time render it difficult to trace the transitions and analogies of forms in the graphic representations belonging to different centuries.

Each branch of a curve has its history, but this history does not reach further back among the nations of the West than the memorable epoch of the 13th of September, 1492, when the re-discoverer of the New World found a line of no variation 3 degrees west of the meridian of the island of Flores, one of the Azores.*

[footnote] *I have elsewhere shown that, from the documents which have come down to us regarding the voyages of Columbus, we can, with much certainty, fix upon three places 'in the Atlantic line of no declination' for the 13th of September, 1492, the 21st of May, 1496, and the 16th of August, 1498. The Atlantic line of no declination at that period ran from northeast to southwest. It then touched the South American continent a little east of Cape Codera, while it is not observed to reach that continent on the northern coast of the Brazils. (Humboldt, 'Examen Critique de l'Hist. de la Geogr.', t. iii., p. 44-48.) From Gilbert's 'Physiologia Nova de Magnete', we see plainly (and the fact is very remarkable) that in 1600 the declination was still null in the region of the Azores, just as it had been in the time of Columbus (lib. 4, cap. 1). I believe that in my 'Examen Critique' (t. iii., p. 54) I have proved from documents that the celebrated line of demarkation by which Pope Alexander VI. divided the Western hemisphere between Portugal and Spain was not drawn through the most western point of the Azores, because Columbus wished to convert a physical into a political division. He attached great importance to the zone (raya) "in which the compass shows no variation, where air and ocean, the later covered with pastures of sea-weed, exhibit a peculiar constitution, where cooling winds begin to blow, and where [as erroneous observations of the polar star led him to imagine] the form (sphericity) of the Earth is no longer the same."

The whole of Europe, excepting a small p 182 part of Russia, has now a western declination, while at the close of the seventeenth century the needle first pointed due north, in London in 1657, and in Paris in 1669, there being thus a difference of twelve years, notwithstanding the small distance between these two places. In Eastern Russia, to the east of the mouth of the Volga, of Saratow, Nischni-Nowgorod, and Archangel, the easterly declination of Asia is advancing toward us. Two admirable observers, Hansteen and Adolphus Erman, have made us acquainted with the remarkable double curvature of the lines of declination in the vast region of Northern Asia; these being concave toward the pole between Obdorsk, on the Oby, and Turuchansk, and convex between the Lake of Baikal and the Gulf of Ochotsk. In this portion of the earth, in northern Asia, between the mountains of Werchojansk, Jakutsk, and the northern Korea, the isogonic lines form a remarkable closed system. This oval configuration* recurs regularly and over a great extent of the South Sea, almost as far as the meridian of Pitcairn and the group of the Marquesas Islands, between 20 degrees north and 45 degrees p 183 south lat.

[footnote] *To determine whether the two oval systems of isogonic lines, so singularly included each within itself, will continue to advance for centuries in the same inclosed form, or will unfold and expand themselves, is a question of the highest interest in the problem of the physical causes of terrestrial magnetism. In the Eastern Asiatic nodes the declination increases from without inward, while in the node or oval system of the South Sea the opposite holds good; in fact, at the present time, in the whole South Sea to the east of the meridian of Kamt-schatka, there is no line where the declination is null, or, indeed, in which it is less than 2 degrees (Erman, in Pogg., 'Annal.', bd. xxxi, 129). Yet Cornelius Schouten, on Easter Sunday, 1616, appears to have found the declination null somewhere to the southeast of Nukahiva, in 15 degrees south lat. and 132 degrees west long., and consequently in the middle of the present closed isogonal system. (Hansteen, 'Magnet. der Erde', 1819 § 28.) It must not be forgotten, in the midst of all these considerations, that we can only follow the direction of the magnetic lines in their progress as they are projected upon the surface of the Earth.

One would almost be inclined to regard this singular configuration of closed, almost concentric, lines of declination as the effect of a local character of that portion of the globe; but if, in the course of centuries, these apparently isolated systems should also advance, we must suppose, as in the case of all great natural forces, that the phenomenon arises from some general cause.

The horary variations of the declination, which, although dependent upon true time, are apparently governed by the Sun, as long as it remains above the horizon, diminish in angular value with the magnetic latitude of place. Near the equator, for instance, in the island of Rawak, they scarcely amount to three or four minutes, while they are from thirteen to fourteen minutes in the middle of Europe. As in the whole northern hemisphere the north point of the needle moves from east to west on an average from 8 1/2 in the morning until 1 1/2 at mid-day, while in the southern hemisphere the same north point moves from west to east,* attention has recently been drawn, with much justice, to the fact that there must be a region of the Earth between the terrestrial and the magnetic equator where no horary deviations in the declination are to be observed.

[footnote] *Arago, in the 'Annuaire', 1836, p. 284, and 1840, p. 330-338.

This fourth curve, which might be called the 'curve of no motion', or, rather, 'the line of no variation of horary declination', has not yet been discovered.

The term 'magnetic poles' has been applied to those points of the Earth's surface where the horizontal power disappears, and more importance has been attached to these points than properly appertains to them;* and in like manner, the curve, where the inclination of the needle is null, has been termed the 'magnetic equator'.

[footnote] *Gauss, 'Allg. Theorie des Erdmagnet.', 31.

The position of this line and its secular change of configuration have been made an object of careful investigation in modern times. According to the admirable work of Duperrey,* who crossed the magnetic equator six times between 1822 and 1825, the nodes of the two equators, that is to say, the two points at which the line without inclination intersects the terrestrial equator, and consequently passes from one henisphere into the other, are so unequally placed, that in 1825 the node near the island of St. Thomas, on the western p 184 coast of Africa, was 188 1/2 degrees distant from the node in the South Sea, close to the little islands of Gilbert, nearly in the meridian of the Viti group.

[footnote] *Duperrey, 'De la Configuration de l'Equateur Magnetique', in the 'Annales de Chimie', t. xlv., p. 371 and 379. (See also, Morlet, in the 'Memoires presentes par divers Savans a l'Acad. Roy. des Sciences', t. iii., p. 132.

In the beginning of the present century, at an elevation of 11,936 feet above the level of the sea, I made an astronomical determination of the point (7 degrees 1' south lat., 48 degrees 40' west long. from Paris), where, in the interior of the New Continent, the chain of the Andes is intersected by the magnetic equator between Quito and Lima. To the west of this point, the magnetic equator continues to traverse the South Sea in the southern hemisphere, at the same time slowly drawing near the terrestrial equator. It first passes into the northern hemisphere a little before it approaches the Indian Archipelago, just touches the southern points of Asia, and enters the African continent to the west of Socotora, almost in the Straits of Bab-el-Mandeb, where it is most distant from the terrestrial equator. After intersecting the unknown regions of the interior of Africa in a southwest direction, the magnetic equator re-enters the south tropical zone in the Gulf of Guinea, and retreats so far from the terrestrial equator that it touches the Brazilian coast near Os Ilheos, north of Porto Seguro, in 15 degrees south lat. From thence to the elevated plateaux of the Cordilleras, between the silver mines of micuipampa and Caxamarca, the ancient seat of the Incas, where I observed the inclination, the line traverses the whole of South America, which in these latitudes is as much a magnetic 'terra incognita' as the interior of Africa.

The recent observations of Sabine* have shown that the node near the island of St. Thomas has moved 4 degrees from east to west between 1825 and 1837.

[footnote] *See the remarkable chart of isoclinic lines in the Atlantic Ocean for the years 1825 and 1837, in Sabine's 'Contributions to Terrestrial Magnetism', 1840, p. 134.

It would be extremely important to know whether the opposite pole, near the Gilbert Islands, in the South Sea, has aproached the meridian of the Carolinas in a westerly direction. These general remarks will be sufficient to connect the different systems of isoclinic non-parallel lines with the great phenomenon of equilibrium which is manifested in the magnetic equator. It is no small advantage, in the exposition of the laws of terrestrial magnetism, that the magnetic equator (whose oscillatory change of form and whose nodal motion exercise an influence on the inclination of the needle in the remotest districts of the world, in consequence of the altered magnetic latitudes)* should traverse the p 185 ocean throughout its whole course, excepting about one fifth, and consequently be made so much more accessible, owing to the remarkable relations in space between the sea and land, and to the means of which we are now possessed for determining with much exactness both the declination and the inclination at sea.

[footnote] *Humboldt, 'Ueber die seculäre Veränderung der Magnetischen Inclination' (On the secular Change in the Magnetic Inclination), in Pogg. 'Annal.', bd. sv., s. 322.

We have described the distribution of magnetism on the surface of our planet according to the two forms of 'declination' and 'inclination'; it now, therefore, remains for us to speak of the 'intensity of the force' which is graphically expressed by isodynamic curves (or lines of equal intensity). The investigation and measurement of this force by the oscillations of a vertical or horizontal needle have only excited a general and lively interest in its telluric relations since the beginning of the nineteenth century. The application of delicate optical and chronometrical instruments has rendered the measurement of this horizontal power susceptible of a degree of accuracy far surpassing that attained in any other magnetic determinations. The isogonic lines are the more important in their immediate application to navigation, while we find from the most recent views that isodynamic lines, especially those which indicate the horizontal force, are the most valuable elements in the theory of terrestrial magnetism.*

[footnote] *Gauss, 'Resultate der Beob. des Magn. Vereins', 1838, 21; Sabine, 'Report on the Variations of the Magnetic Intensity', p. 63.

One of the earliest facts yielded by observation is, that the intensity of the total force increases from the equator toward the pole.*

[footnote] *The following is the history of the discovery of the law that the intensity of the force increases (in general) with the magnetic latitude. When I was anxious to attach myself, in 1798, to the expedition of Captain Bandin, who intended to circumnavigate the globe, I was requested by Borda, who took a warm interest in the success of my project, to examine the oscillations of a vertical needle in the magnetic meridian in different latitudes in each hemisphere, in order to determine whether the intensity of the force was the same, or whether it varied in different places. During my travels in the tropical regions of America, I paid much attention to this subject. I observed that the same needle, which in the space of ten minutes made 245 oscillations in Paris, 246 in the Havana, and 242 in Mexico, performed only 216 oscillations during the same period at St. Carlos del Rio Negro (1 degree 53' north lat. and 80 degrees 40' west long. from Paris), on the magnetic equator, i.e., the line in which the inclination =0; in Peru (7 degrees 1' south lat. and 80 degrees 40' west long. from Paris) only 211;while at Lima (12 degrees 2' south lat.) the number rose to 219. I found, in the years intervening between 1799 and 1803, that the whole force, if we assume it at 1.0000 on the magnetic equator in the Peruvian Andes, between Micuipampa and Caxamarca, may be expressed at Paris by 1.3482, in Mexico by 1.3155, in San Carlos del Rio Negro by 1.0480, and in Lima by 1.0773. When I developed this law of the variable intensity of terrestrial magnetic force, and supported it by the numerical value of observations instituted in 104 different places, in a Memoir read before the Paris Institute on the 26th Frimaire, An. XIII. (of which the mathematical portion was contributed by M. Biot), the facts were regarded as altogether new. It was only after the reading of the paper, as Biot expressly states (Lametherie, 'Journal de Physique', t. lix., p. 446, note 2) and as I have repeated in 'the Relation Historique', t. i., p. 262, note 1, that M. de Rossel communicated to Biot his oscillation experiments made six years earlier (between 1791 and 1794) in Van Diemen's Land, in Java, and in Amboyna. These experiments gave evidence of the same law of decreasing force in the Indian Archipelago. It must, I think be supposed, that this excellent man, when he wrote his work, was not aware of the regularity of the augmentation and diminution of the intensity as before the reading of my paper he never mentioned this (certainly not unimportant) physical law to any of our mutual friends, La Place, Delambre, Prony, or Biot. It was not till 1808, four years after my return from America that the observations made by M. de Rossel were published in the 'Voyage de l'Entrecasteaux', t. ii., p. 287 , 291, 321, 480, and 644. Up to the present day it is still usual, in all the tables of magnetic intensity which have been published in Germany (Hausteen, 'Magnet. der Erde', 1819, s. 71; Gauss, 'Beob. des Magnet. Vereins', 1838, s. 36-39; Erman, 'Physikal. Beob.', 1841, s. 529-579), in England (Sabine, 'Report on Magnet. Intensity', 1838, p. 43-62; 'Contributions to Terrestrial Magnetism', 1843), and in France (Becquerel, 'Traite de Electr. et de Magnet.', t. vii., p. 354-367), to reduce the oscillations observed in any part of the Earth to the standard of force which I found on the magnetic equator in Northern Peru, so that, according to the unit thus arbitrarily assumed, the intensity of the magnetic force at Paris is put down as 1.348. The observations made by Lamanon in the unfortunate expedition of La Perouse, during the stay at Teneriffe (1785), and on the voyage to Macao (1787), are still older than those of Admiral Rossel. They were sent to the Academy of Sciences, and it is known that they were in the possession of Condorcet in the July of 1787 (Becquerel, t. vii., p. 320); but, notwithstanding the most careful search, they are not now to be found. From a copy of a very important letter of Lamanon, now in the possession of Captain Duperrey, which was addressed to the then perpetual secretary of the Academy of Sciences, but was omitted in the narrative of the 'Voyage de La Perouse', it is stated "that the attractive force of the magnet is less in the tropics than when we approach the poles, and that the magnetic intensity deduced from the number of oscillations of the needle of the inclination-compass varies and increases with the latitude." If the Academicians, while they continued to expect the return of the unfortunate La Perouse, had felt themselves justified, in the course of 1787, in publishing a truth which had been independently discovered by no less than three different travelers, the theory of terrestrial magnetism would have been extended by the knowledge of a new class of observations, dating eighteen years earlier than they now do. This simple statement of facts may probably justify the observations contained in the third volume of my 'Relation Historique' p. 615): "The observations on the variation of terrestrial magnetism, to which I have devoted myself for thirty-two years, by means of instruments which admit of comparison with one another, in America, Europe, and Asia, embrace an area extending over 188 degrees of longitude, from the frontier of Chinese Dzoungarie to the west of the South Sea bathing the coasts of Mexico and Peru, and reaching from 60 degrees north lat. to 12 degrees south lat. I regard the discovery of the law of the decrement of magnetic force from the pole to the equator as the most important result of my American voyage." Although not absolutely certain, it is very probable that Condorcet read Lamanon's letter of July, 1787, at a meeting of the Paris Academy of Sciences; and such a simple reading I regard as a sufficient act of publication. ('Annuaire du Bureau des Longitudes', 1842, p. 463.) The first recognition of the law belongs, therefore, beyond all question, to the comparison of La Perouse; but, long disregarded or forgotten, the knowledge of the law that the intensity of the magnetic force of the Earth varied with the latitude, did not, I conceive, acquire an existence in science until the publication of my observations from 1798 to 1804. The object and the length of this note will not be indifferent to those who are familiar with the connection with it, and who, from their own experience, are aware that we are apt to attach some value to that which has cost us the uninterrupted labor of five years, under the pressure of a tropical climate, and of perilous mountain expeditions.

p 186 The knowledge which we possess of the quantity of this increase, and of all the numerical relations of the law of intensity p 187 affecting the whole Earth, is especially due, since 1819, to the unwearied activity of Edward Sabine, who, after having observed the oscillations of the same needles at the American north pole, in Greenland, at Spitzbergen, and on the coasts of Guinea and Brazil, has continued to collect and arrange all the facts capable of explaining the direction of the isodynamic system in zones for a small part of South America. These lines are not parallel to lines of equal inclination (isoclinic line), and the intensity of the force is not at its minimum at the magnetic equator, as has been supposed, nor is it even equal at all parts of it. If we compare Erman's observations in the southern part of the Atlantic Ocean, where a faint zone (0.706) extends from Angola over the island of St. Helena to the Brazilian coast, with the most recent investigations of the celebrated navigator James Clark Ross, we shall find that on the surface of our planet the force increases almost in the relation of 1:3 toward the magnetic south pole, where Victoria Land extends from Cape Crozier toward the volcano Erebus, which has been raised to an elevation of 12,600 feet above the ice.*

[footnote] *From the observations hitherto collected, it appears that the maximum of intensity for the whole surface of the Earth is 2.052, and the minimum 0.706. Both phenomena occur in the southern hemisphere; the former in 73 degrees 47' S. lat., and 169 degrees 30'E. long. from Paris, near Mount Crozier, west-northwest of the south magnetic pole, at a place where Captain James Ross found the inclination of the needle to be 87 degrees 11' (Sabine, 'Contributions to Terrestrial Magnetism', 1843, No. 5, p. 231); the latter, observed by Erman at 19 degrees 59' S. lat., and 37 degrees 24' W. long. from Paris, 320 miles eastward from the Brazilian coast of Espiritu Santo (Erman, 'Phys. Beob.', 1841, s. 570), at a point where the inclination is only 7 degrees 55'. The actual ratio of the two intensities is therefore as 1 to 2.906. It was long believed that the greatest intensity of the magnetic force was only two and a half times as great as the weakest exhibited on the Earth's surface. (Sabine, 'Report on Magnetic Intensity', p. 82.)