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not be the form of the earth, because the strata increase in density towards the centre. The lunar inequalities also prove the earth to be so constructed; it was requisite, therefore, to consider the fluid mass to be of variable density. Including this condition, it has been found that the mass, when in rotation, would still assume the form of an ellipsoid of revolution; that the particles of equal density would arrange themselves in concentric elliptical strata, the most dense being in the centre; but that the compression would be less than in the case of the homogeneous fluid. The compression is still less when the mass is considered to be, as it actually is, a solid nucleus, decreasing regularly in density from the centre to the surface, and partially covered by the ocean, because the solid parts, by their cohesion, nearly destroy that part of the centrifugal force which gives the particles a tendency to accumulate at the equator, though not altogether; otherwise the sea, by the superior mobility of its particles, would flow towards the equator and leave the poles dry : besides, it is well known that the continents at the equator are more elevated than they are in higher latitudes. It is also necessary for the equilibrium of the ocean, that its density should be less than the mean density of the earth, otherwise the continents would be perpetually liable to inun
dations from storms and other causes. On the whole, it appears from theory that a horizontal line passing round the earth, through both poles, must be nearly an ellipse, having its major axis in the plane of the equator, and its minor axis coinciding with the axis of the earth's rotation. The intensity of the centrifugal force is measured by the deflection of any point from the tangent in a second, and is determined from the known velocity of the earth's rotation: the force of gravitation at any place is measured by the descent of a heavy body in the first second of its fall. At the equator the centrifugal force is equal to the 289th part of gravity, and diminishes towards the poles as the cosine of the latitude, for the angle between the directions of these two forces, at any point of the surface, is equal to its latitude. But whatever the constitution of the earth and planets may be, analysis proves that, if the intensity of gravitation at the equator be taken equal to unity, the sum of the compression of the ellipsoid and the whole increase of gravitation, from the equator to the pole, is equal to five-halves of the ratio of the centrifugal force to gravitation at the equator. This quantity, with regard to the earth, is şof ty, or 11t;
을 consequently the compression of the earth is equal to nie, diminished by the whole increase of gravitation, so that its form will be known, if the whole increase of gravitation, from the equator to the pole, can be determined by experiment. But there is another method of ascertaining the figure of our planet. It is easy to show, in a spheroid whose strata are elliptical, that the increase in the length of the radii, the decrease of gravitation, and the increase in the lengths of the arcs of the meridian, corresponding to angles of one degree, from the pole to the equator, are proportional to the square
of the cosine of the latitude. These quantities are so connected with the ellipticity of the spheroid, that the total increase in the length of the radii is equal to the compression, and the total diminution in the length of the arcs is equal to the compression multiplied by three times the length of an arc of one degree at the equator, Hence, by measuring the meridian curvature of the earth, the compression, and consequently its figure, become known. This, indeed, is assuming the earth to be an ellipsoid of revolution, but the actual measurement of the globe will show how far it corresponds with that solid in figure and constitution.
The courses of the great rivers, which are in general navigable to a considerable extent, prove that the curvature of the land differs but little from that of the ocean; and as the heights of the mountains and continents are inconsiderable when compared with the magnitude of the earth, its figure is understood to be determined by a surface at every point perpendicular to the direction of gravitation, or of the plumb-line, and is the same which the sea would have if it were continued all round the earth beneath the continents. Such is the figure that has been measured in the following
A terrestrial meridian is a line passing through both poles, all the points of which have their noon contemporaneously. Were the lengths and curvatures of different meridians known, the figure of the earth might be determined; but the length of one degree is sufficient to give the figure of the earth, if it be measured on different meridians, and in a variety of latitudes; for if the earth
; were a sphere, all degrees would be of the same length, but if not, the lengths of the degrees will be greatest where the curvature is least, and will be greater exactly in proportion as the curvature is less; a comparison of the lengths of the degree in different parts of the earth's surface will therefore determine its size and form.
An arc of the meridian may be measured by observing the latitude of its extreme points, and then measuring the distance between them in feet or fathoms : the distance thus determined on the surface of the earth, divided by the degrees and
parts of a degree contained in the difference of the latitudes, will give the exact length of one degree, the difference of the latitudes being the angle contained between the verticals at the extremities of the arc. This would be easily accomplished were the distance unobstructed, and on a level with the sea ; but on account of the innumerable obstacles on the surface of the earth, it is necessary to connect the extreme points of the arc by a series of triangles, the sides and angles of which are either measured or computed, so that the length of the arc is ascertained with much laborious computation. In consequence of the irregularities of the surface, each triangle is in a different plane; they must therefore be reduced by computation to what they would have been, had they been measured on the surface of the sea; and as the earth may in this case be esteemed spherical, they require a correction to reduce them to spherical triangles.
Arcs of the meridian have been measured in a variety of latitudes north and south, as well as arcs perpendicular to the meridian. From these measurements it appears that the lengths of the degrees increase from the equator to the poles, nearly in proportion to the square of the sine of the latitude; consequently the convexity of the earth diminishes from the equator to the poles.
Were the earth an ellipsoid of revolution, the