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Pope.

Sudden he viewed, in spite of all her art, An earthly lover lurking at her heart. Now scarce withdrawn the fierce earthshaking power, Jove's daughter Pallas watched the fav'ring hour; Back to their caves she bade the winds to fly, And hushed the blustering brethren of the sky. Id. Poor, earth-created man! Young.

a thousand furies more did shake

Those weary realms, and kept earth-loving man awake. Armstrong. It is no uncommon thing for the honour of an earthly monarch to be wounded through the sides of Mason.

his ministers.

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The purity of heaven to earthly joys, Expel the venom and not blunt the dartThe dull satiety which all destroys-

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6

The EARTH, in astronomy, is one of the primary planets. See ASTRONOMY. Although the relative densities of the earth and most of the other planets have been known a considerable time, it is but very lately that we have come to the knowledge of the absolute gravity or density of the whole mass of the earth. This, says Dr. Hutton, I have calculated and deduced from the observations of Dr. Maskelyne, astronomer royal, at the mountain Schehallien in the years 1774, 5, and 6. The attraction of that mountain on a

plummet, being observed on both sides of it, and tions in all directions, and consisting of stone; these its mass being computed from a number of secdata being then compared with the known attraction and magnitude of the earth, gave by proportion its mean density; which is to that of water as nine to two, and to common stone as nine to five; from which very considerable mean density,

it may be presumed, that the internal parts contain great quantities of metals. From the density now found,' adds this writer,' its quantity of matter becomes known, being equal to the product of its density by its magnitude.'

Mr. Boyle suspected that there are great, though slow, internal changes, in the mass of the earth. He argues from the varieties observed in the change of the magnetic needle, and from the observed changes in the temperature of climates. But as to the latter, there is reason to doubt that he could not have diaries of the weather sufficient to direct his judgment. Boyle's Works, Abr. Vol. I, p. 292, &c.

Respecting the figure of the earth, the ancients had various opinions: some, as Anaximander and Leucippus, held it cylindrical, or in the form of a drum: but the most general opinion was, that it was flat; that the visible horizon was the boundary of the earth, and the ocean the boundary of the horizon: that the heavens and earth above this ocean were the whole visible universe and that all beneath the ocean was Hades. Of this opinion were some of the Christian fathers, as Lactantius, St. Augustine, &c. Such of the ancients, however, as understood any thing of astronomy, and especially the doctrine of eclipses, must have been acquainted with the circular figure of the earth; as the ancient Babylonian astronomers, who had calculated eclipses long before the time of Alexander, and Thales the Grecian, who predicted an eclipse of the sun. It is now indeed agreed on all hands, that the form of the terraqueous globe is globular or very nearly so. See ASTRONOMY. This is equally evident from the eclipses of the sun and of the moon; in all of which the earth's shadow appears circular upon the face of those bodies, what way soever it be projected, whether east, west, north, or south; and howsoever its diameter vary,

And root from out the soul the deadly weed which according to the greater or less distance from the

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earth. The spherical figure of the earth is also

evinced from the rising and setting of the sun, moon, and stars; all which happen sooner to those who live to the east and later to those living to the west, and that more or less so, according to the distance. So also, going or sailing to the north, the north-pole and northern stars become more elevated, and the south-pole and southern stars more depressed; the elevation northerly increasing equally with the depression southerly; and either of them proportionably to the distance gone. The same thing happens in going to the south. Besides, the oblique ascensions, descensions, emersions, and amplitudes of the rising and setting of the sun and stars, in every latitude, are agreeable to the earth's spherical form: all which could not happen if it were of any other figure. The globular form of the earth is farther confirmed by its having been often sailed round: the first of these important voyages was made in 1519, by Ferdinand Magellan, who accomplished it in 1124 days. In 1557 Sir Francis Drake performed the same voyage in 1056 days: in 1586 Sir Thomas Cavendish performed it in 777 days; Simon Cordes, of Rotterdam, in 1590, in 1575 days: in 1598 Oliver Noort, a Hollander, in 1077 days; Van Schouten, in 1615, in 749 days; Jacob Heremites and John Huygens, in 1623, in 802 days. Many others have since performed it, particularly Anson, Bougainville, and Cook; sometimes sailing round by the east sometimes by the west, till at length they arrived again in Europe, whence they set out; and, in the course of their voyage, observed that all the phenomena, both of the heavens and the earth, correspond to, and prove this spherical figure.

The natural cause of this form of the globe is, according to Sir Isaac Newton, the great principle of attraction, with which the Creator has endued all the matter in the universe; and by which all bodies, and all the parts of bodies, mutually attract one another. This is also the cause of the sphericity of the drops of rain, quicksilver, &c. The inequality of the surface of the earth, by mountains and valleys, is nothing considerable; the highest eminence being scarcely equivalent in its proportion to the bulk of the earth to the minutest protuberance on the surface of an orange. Its difference from a perfect sphere, however, is more considerable in another respect, by which it approaches nearly to the shape of an oblate spheroid; being a little flatted at the poles, and raised about the equatorial parts, so that the axis from pole to pole is less than the equatorial diameter. What gave the first occasion to the discovery of this important circumstance was, the observations of some French and English philosophers in the East Indies, and other parts, who found that pendulums, the nearer they came to the equator, performed their vibrations slower: whence it follows, that the velocity of the descent of bodies, by gravity, is less in countries nearer to the equator; and consequently that those parts are farther removed from the centre of the earth, or from the common centre of gravity. See the History of the Royal Academy of Sciences, by Du Hamel, p. 110, 156, 206; and L'Ilistoire de l'Academie Roy. 1700 and 1701. These observations having established the fact also stimulated M. Huygens and Sir Isaac Newton to in

vestigate the cause of this phenomenon; which they attributed to the revolution of the earth about its axis. If the earth were in a fluid state, its rotation round its axis would necessarily make it put on such a figure, because, the centrifugal force being greatest towards the equator, the fluid would there rise and swell most; and, that its figure really should be so now, seems necessary, to keep the sea in the equinoctial regions from overflowing the earth about those parts. See this curious subject well treated by Huygens, in his discourse De Causâ Gravitatis, p. 154, where he states the ratio of the polar diameter to that of the equator, as 577 to 578. And Newton, in his Principia, first published in 1686, demonstrates from the theory of gravity, that the figure of the earth must be that of an oblate spheroid, generated by the rotation of an ellipse about its shortest diameter, provided all the parts of the earth were of a uniform density. throughout; and that the proportion of the polar to the equatorial diameter of the earth, would be that of 689 to 692, or nearly that of 229, to 230, or as 9956522 to 1. This proportion of the two diameters was calculated by Newton in the following manner: having found that the centrifugal force at the equator is of gravity, he assumes, as an hypothesis, that the earth is to the diameter of the equator as 100 to 101, and thence determines what must be the centrifugal force at the equator to give the earth such a form, and finds it to be of gravity: then, by proportion, if a centrifugal force equal to of gravity would make the earth higher at the equator than at the poles by of the whole height at the poles, a centrifugal force that is of gravity will make it higher by a proportional excess, which by calculation is of the height at the poles; and thus he discovered, that the diameter at the equator is to the diameter at the poles, or the axis, as 230 to 229. But this computation supposes the earth to be every where of a uniform density; whereas if the earth is more dense near the centre, then bodies at the poles will be more attracted by this additional matter being nearer; and therefore the excess of the semi-diameter of the equator above the semi-axis, will be different. According to this proportion between the two diameters, Newton farther computes, from the different measures of a degree, that the equatorial diameter will exceed the polar by thirty-four miles and. Nevertheless, Messrs. Cassini, both father and son, the one in 1701, and the other in 1713, attempted to prove, in the Memoirs of the Royal Academy of Sciences, that the earth was an oblong spheroid: and in 1718, M. Cassini again undertook, from observations, to show that, on the contrary, the longest diameter passes through the poles; which gave occasion for Mr. John Bernouilli, in his Essai d'une Nouvelle Physique Celeste, printed at Paris in 1735, to triumph over the British philosopher, apprehending that these observations would invalidate what Newton had demonstrated. And in 1720 M. De Mairan advanced arguments, supposed to be strengthened by geometrical demonstrations, farther to confirm the assertions of Cassini. But in 1735 two companies of mathematicians were employed, one for a northern, and another for a southern expedition,

earth's figure, and for the ellipticity of the homogeneous spheroid,

P-II
II

2-: therefore 2

P-
n

the result of whose observations and measurement plainly proved that the earth was flatted at the poles. The proportion of the equatorial diameter to the polar, as stated by the gentlemen employed on the northern expedition for mea- and, therefore, according to your observation, suring a degree of the meridian, is as 1 to 0-9891; This is the just conclusion from your by the Spanish mathematicians as 266 to 265, or observations of the pendulum, taking it for as 1 to 0-99624: by M. Bouguer as 179 to 178, granted that the meridians are ellipses: which is or as 1 to 0.99441. As to all conclusions, howan hypothesis upon which all the reasonings ever, deduced from the length of pendulums in of theory have hitherto proceeded. But, plausidifferent places, it is to be observed, that they ble as it may seem, I must say that there is much proceed upon the supposition of the uniform reason from experiment to call it in question. density of the earth, which is a very improbable If it were true, the increment of the force which circumstance; as justly observed by Dr. Horsley actuates the pendulum as we approach the poles, in his letter to captain Phipps: you finish your should be as the square of the sine of the latitude: article, he concludes, relating to the pendulum or, which is the same thing, the decrement, as with saying, 'that these observations give a figure we approach the equator, should be as the square of the earth nearer to Sir Isaac Newton's com- of the cosine of the latitude. But whoever takes putation, than any others that have hitherto been the pains to compare together such of the obsermade;' and then you state the several figures vations of the pendulum in different latitudes, as given, as you imagine, by former observations, seem to have been made with the greatest care, and by your own. Now it is very true, that, if will find that the increments and decrements do the meridians be ellipses, or if the figure of the by no means follow these proportions; and, in earth be that of a spheroid generated by the those which I have examined, I find a regularity revolution of an ellipsis, turning on its shorter in the deviation which little resembles the mere axis, the particular figure, or the ellipticity of error of observation. The unavoidable concluthe generating ellipsis, which your observations sion is, that the true figure of the meridians is give, is nearer to what Sir Isaac Newton saith it not elliptical. If the meridians are not ellipses, should be, if the globe were homogeneous, than the difference of the diameters may indeed, or it any that can be derived from former observations. may not, be proportioned to the difference beBut yet it is not what you imagine. Taking the tween the polar and the equatorial force; but gain of the pendulum in latitude 79° 50' exactly it is quite an uncertainty, what relation subas you state it, the difference between the equa- sists between the one quantity and the other; torial and the polar diameter is about as much our whole theory, except so far as it relates to the less than the Newtonian computation makes it, homogeneous spheroid, is built upon false asand the hypothesis of homogeneity would re- sumptions, and there is no saying what figure of quire, as you reckon it, to be greater. The pro- the earth any observations of the pendulum give.' portion of 212 to 211 should indeed, according Dr. Horsley then lays down the following table, to your observations, be the proportion of the which shows the different results of observations force that acts upon the pendulum at the poles to made in different latitudes; in which the first the force acting upon it at the equator. But this is three columns contain the names of the obserby no means the same with the proportion of the vers, the places of observation, and the latitude equatorial diameter to the polar. If the globe were of each; the fourth column shows the quantity homogeneous the equatorial diameter would ex- of P- -II in such parts as II is 100,000, as deceed the polar by of the length of the latter: duced from comparing the length of the penduand the polar force would also exceed the equa- lum, at each place of observation, with the length torial by the like part. But, if the difference be- of the equatorial pendulum as termed by M. tween the polar and equatorial force be greater than Bouguer, upon the supposition that the incre(which may be the case in an heterogeneous ments and decrements of force, as the latitude is globe, and seems to be the case in ours), then increased or lowered, observe the proportion the difference of the diameters should, according which theory assigns. Only the second and the to theory, be less than, and vice versa, I last value of P-II are concluded from comconfess this is by no means obvious, at first parisons with the pendulum at Greenwich and sight; so far otherwise, that the mistake, which at London, not at the equator. The fifth column you have fallen into, was once very general. shows the value of ♪ corresponding to every value Many of the best mathematicians were misled of P-II, according to Clairault's theorem : by too implicit a reliance upon the authority of Newton, who had certainly confined his investigations to the homogeneous spheroid, and had thought about the heterogeneous only in a loose and general way. The late Mr. Clairault was the first who set the matter right, in his elegant and subtle treatise on the figure of the earth. That work has now been many years in the hands of mathematicians, among whom I imagine there are none, who have considered the subject attentively, that do not acquiesce in the author's conclusions. In the second part of that treatise, it is proved, that putting P for the polar force, II for the equatorial, & for the true ellipticity of the

Observers.

Bouguer
Bouguer
Green
Bouguer
Abbé de La

Caille
The Acade-

micians

Capt. Phipps

Places.

Lat. P-II. 8

Equator
Porto Bello
Otaheitee

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9

34 741-8

17

29 563-2 326

San Domingo 18
Cape of

27 591.08

Good Hope 33 55731-5

Paris

Pello

48

50 585-11

66 48 565 9 39

79 50471-2231

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joined, and mo drawn parallel to a C: Co is the cosine of the latitude to the radius CP, and CY that cosine augmented in the ratio before named; YQ being to Yl, that is, Ca to Cn, or CP, as the tangent of the angle YCQ, the latitude of the point E to the tangent of the angle YC belonging to the augmented cosine. Thus, if M represent the measure in a latitude denoted by E, and N the measure at the equator, let A denote an angle whose measure is

M

Then

tan. A tan. E

is =

less axis

greater axis

cos. Ex3√ N
But M, or the length of a degree, obtained by
actual mensuration in different latitudes, is known
from the following table:—

Name.

Maupertuis, &c.
Cassini and
La Caille
Boscovich

De la Caille
Juan and Ulloa
Bouguer
Condamine

Lat.

Value of M.

Toises. M57438 M = 57074

M57050

66° 20'

49 22

45 00

43 00

M = 56972

33 18

M 57037

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By this table it appears, that the observations in the middle parts of the globe, setting aside the single one at the Cape, are as consistent as could reasonably be expected; and they represent the ellipticity of the earth as about. But when we come within ten degrees of the equator, it should seem that the force of gravity suddenly becomes much less, and within the like distance of the poles much greater than it could be in such a spheroid.' The following problem communicated by Dr. Leatherland to Dr. Pemberton, and published by Mr. Robertson, serves to find the proportion between the axis and the equatorial diameter, from measures of a degree of the meridian in two different latitudes, supposing the earth an oblate spheroid. Let A Pap (Pl. 124, fig. 1.) be an ellipse representing a section of the earth through the axis Pp; the equatorial diameter, or the greater axis of the ellipse, being Aa; let E and F be two places, where the measure of a degree has been taken; these measures are proportional to the radii of curvature in the ellipse at those places; and if CQ, CR, be conjugates to the diameters whose vertices are E and F, CQ will be to CR in the subtriplicated ratio of the radius of curvature at E to that at F, by Cor. 1, Prop. 4, part 6, of Milnes's Conic Sections, and therefore in a given ratio to one another; also the angles QCP, RCP, are the latitudes of E and F; so that, drawing QV pa. rallel to PP, QXY W to Aa, these angles being Now, by comparing the first with each of the given, as well as the ratio of CQ to CR, the following ones; the second with each of the folrectilinear figure CVQXRY is given in species; lowing; and in like manner the third, fourth, and and the ratio of VC2. -ZC2 (= QX X XW) fifth, with each of the following; there will be to RZ-QV2 (RX x XS) is given, which obtained twenty-five results, each showing the is the ratio of CA2 to CP2; therefore the ratio relation of the axes or diameters; the arithmetiof CA to CP is given. Hence, if the sine and cal means of all of which will give that ratio as cosine of the greater latitude be each augmented 1 to 0.9951989. If the measures of the latitude in the subtriplicate ratio of the measure of the of 49° 22′, and of 45° which fall within the degree in the greater latitude to that in the lesser, meridian line drawn through France, and which then the difference of the squares of the aug- have been re-examined and corrected since the mented sine, and the sine of the lesser latitude, northern and southern expedition, be compared will be to the difference of the squares of the co- with those of Maupertuis and his associates in sine of the lesser latitude, and the augmented the north, and that of Bouguer at the equator cosine, in the duplicate ratio of the equatorial there will result six different values of the ratio to the polar diameter. For Cq being taken in of the two axes: the arithmetical mean of all CQ equal to CR, and qv drawn parallel to QV, which, is that of 1 to 0-9953467, which may be Cv, and vg, CZ and ZR will be the sines and considered as the ratio of the greater axis to the cosines of the respective latitudes to the same less: which is as 230 to 228-92974, or 215 to radius; and CV, VQ, will be the augmentations 214, or very near the ratio as assigned by Newof Cv and Cq in the ratio named. ton. Hence, to find the ratio between the two axes of the earth, let E denote the greater, and F the lesser of the two latitudes, M and N the respective measures taken in each; and let P denote 34

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P2 x sin. 2E-sin. 2F It also appears from the above problem, that when one of the degrees measured is at the equator, the cosine of the latitude of the other being augmented in the subtriplicate ratio of the degrees, the tangent of the latitude will be to the tangent answering to the augmented cosine,' in the ratio of the greater axis to the less. For, supposing E the place out of the equator, then, if the semi-circle Plmnp be described, and IC

Now the magnitude, as well as the figure of the earth, that is, the polar and equatorial diameters, may be deduced from the foregoing problem. For, as half the latus rectum of the greater axis A a is the radius of curvature at A, it is given in magnitude from the degree measured there, and thence the axes themselves are given. Thus, the circular arc whose length is equal to the radius being 57-29578 degrees, if this number be multiplied by 56750 toises, the measure of a degree at the equator, as Bouguer has stated it, the product will be the radius of cur vature there, or half the latus rectum of the greater axis; and this is to half the less axis in the ratio of the less axis to the greater, that is, as 0-9953467 to 1; whence the two axes are 6533820 and 6564366 toises, or 7913 and 7950 English miles: and the differences between the two axes about thirty-seven miles. See Robertson's Navi

gation, vol. ii. p. 206, &c. Suite des Mem. de l'Acad. 1718, p. 247, and Maclaurin's Fluxions vol. II. book i. chap. xiv. And very nearly the same ratio is deduced from the lengths of pendulums vibrating in the same time, in different latitudes; provided it be again allowed, that the meridians are real ellipses, or the earth a true spheroid, which, however, can only take place in the case of a uniform gravity in all parts of the earth. Thus, in the new Petersburgh Acts, for 1788 and 1789, are accounts and calculations of experiments relative to this subject, by M. Krafft. These experiments were made at different times and in various parts of the Russian empire. This gentleman has collected and compared them, and drawn the proper conclusions from them: thus, he infers, that the length of a pendulum that swings seconds in any given latitude A, and in a temperature of 10° of Reaumur's thermometer may be determined by this equation :

foot, or a

439·1782-321 sine X, lines of a French

39.0045 +0-206 sine X, in English, inches, in the temperature of 53 of Fahrenheit's thermometer. This expression nearly agrees, not only with all the experiments made on the pendulum in Russia, but also with those of Mr. Graham in England, and those of Mr. Lyons in 79° 50′ N. lat., where he found its length to be 431-38 lines. It also shows the augmentation of gravity from the equator to the parallel of a given latitude : for, putting g for the gravity under the equator, G for that under the pole, and y for that under the latitude A, M. Krafft finds y = (1 +0·0052848 sine λ) g; and therefore G 10052848 g. From this proportion of gravity under different latitudes, the same author infers, that, in case the earth is a homogeneous ellipsoid, its oblateness must be instead of ; which ought to be the result of this hypothesis; but on the supposition that the earth is a heterogeneous ellipsoid, he finds its oblateness, as deduced from these experiments, to be ; which agrees with that resulting from the measurement of some of the degrees of the meridian. This confirms an observation of M. De la Place, that if the hypothesis of the earth's homogeneity be given up, then the theory, the measurement of degrees of latitude, and experiments with the pendulum, all agree in their result with respect to the oblateness of the earth. See Memoires de l'Acad. 1783, p. 17. In the Philos. Trans. for 1791, p. 236, Mr. Dalby has given some calculations on measured degrees of the meridian, from whence he infers, that those degrees measured in middle latitudes, will answer nearly to an ellipsoid whose axes are in the ratio assigned by Newton, viz. that of 230 to 229. And as to the deviations of some of the others, viz. towards the poles and equator, he thinks they are caused by the errors in the observed celestial arcs.

The cosmogony, or knowledge of the original formation of the earth, the materials of which it was composed, and by what means they were disposed in the order in which we see them, is a subject, which, though perhaps beyond the reach of human sagacity, has exercised the ingenuity of philosophers in all ages. To enter into the

various theories that have been formed upon this subject, would, however, not only swell this article beyond our bounds, but be fatiguing to many readers. As far as human industry has hitherto penetrated, it has been found that the substances of which the earth is composed are neither ranged in a regular series, according to their specific gravities, nor yet thrown together in total disorder, as if by accident or chance. But the depth of the earth, from the surface to the centre, is nearly 4000 miles; and yet the deepest mine in Europe, that at Cotteberg, in Hungary, is not more than 1000 yards deep; so that little is as yet known of its interior parts. From what has been discovered, however, of those parts which lie most contiguous to our observation, naturalists have compared the structure of the earth to the coats of an onion, or the leaves of a book. And indeed, except in some of those immense mountains which have existed from the creation, or at least from the deluge, where the matter, from whatever cause, is more homogeneous, the earth is found to consist of various strata or layers, which differ according to the circumstances of climate and situation. The surface generally consists of a confused mixture of decayed animal and vegetable substances and earths rudely united together but, upon digging below this surface, the materials of the globe are found arranged in a more regular manner. Heaps of stone are indeed frequently found, which do not consist of layers, but are confused masses of unequal thickness and are called rocks. The strata are generally extended through a whole country, and perhaps, with some interruptions and varieties, through the globe itself. When the country is flat, these extensive bodies are found most regular, being in that case nearly parallel to the horizon, though often dipping downwards in a certain angle; in many places the beds have a wave, as where the country consists of gently waving hills and vales; and here also they in general dip. In passing over the ground the soil is found, perhaps to the extent of a mile, mostly composed of sand; and perhaps for another it consists chiefly of clay: which is occasioned by the edges of the different strata lying with an obliquity to the horizon. By a similar projection, mountains, or ridges of mountains, are produced which commonly have what is called a back and a face, the former smoother, and the latter more rugged. It is generally found, also, that the ascent is more gradual on the one side of a mountain than on the other; and this is occasioned by the strata, which have risen above the general level of the country, being abruptly broken off. The order, number, situation with respect to the horizon, depth, intersections, fissures, color, consistence, &c., of these strata have been considered by Dr. Woodward with great attention. The origin and formation of them all is ascribed by him to the deluge. He supposes that, at that dreadful revolution, all sorts of terrestrial bodies had been dissolved and mixed with the waters, forming altogether, a chaos or confused mass; and he also supposes, that this mass of terrestrial particles, intermixed with water, was at length precipitated to the bottom; and that, in general, according to the order of gravity, the

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