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Planets sometimes eclipse one another. On the 17th of May, 1737, Mercury was eclipsed by Venus near their inferior conjunction: Mars passed over Jupiter on the 9th of January, 1591, and on the 13th of October, 1825, the moon eclipsed Saturn. These phenomena, however, happen very seldom, because all the planets, or even a part of them, are very rarely seen in conjunction at once; that is, in the same part of the heavens at the same time. More than 2500 years before our era, the five great planets were in conjunction. On the 15th of September, 1186, a similar assemblage took place between the constellations of Virgo and Libra; and in 1801, the Moon, Jupiter, Saturn, and Venus were united in the heart of the Lion. These conjunctions are so rare, that Lalande has computed that more than seventeen millions of millions of years separate the epochs of the contemporaneous conjunctions of the six great planets.
The motions of the moon have now become of more importance to the navigator and geographer than those of any other heavenly body, from the precision with which the longitude is determined by the occultations of stars and lunar distances. The occultation of a star by the moon is a phenomenon of frequent occurrence: the moon seems to pass over the star, which almost instantaneously vanishes at one side of her disc, and
after a short time as suddenly reappears on the other; and a lunar distance is the observed distance of the moon from the sun, or from a particular star or planet, at any instant. The lunar theory is brought to such perfection, that the times of these phenomena, observed under any meridian, when compared with those computed for Greenwich in the Nautical Almanac, give the longitude of the observer within a few miles. The accuracy of that work is obviously of extreme importance to a maritime nation: we have reason to hope that the new Ephemeris, now in preparation, will be by far the most perfect work of the kind that ever has been published.
From the lunar theory, the mean distance of the sun from the earth, and thence the whole dimensions of the solar system, are known; for the forces which retain the earth and moon in their orbits are respectively proportional to the radii vectores of the earth and moon, each being divided by the square of its periodic time; and as the lunar theory gives the ratio of the forces, the ratio of the distances of the sun and moon from the earth is obtained; whence it appears that the sun's mean distance from the earth is nearly 396 times greater than that of the moon. The method, however, of finding the absolute distances of the celestial bodies in miles, is in fact the same with
that employed in measuring the distances of terrestrial objects. From the extremities of a known base, the angles which the visual rays from the object form with it are measured; their sum subtracted from two right angles gives the angle opposite the base; therefore, by trigonometry, all the angles and sides of the triangle may be computed-consequently the distance of the object is found. The angle under which the base of the triangle is seen from the object is the, parallax of that object; it evidently increases and decreases with the distance; therefore the base must be very great indeed to be visible at all from the celestial bodies. The globe itself, whose dimensions are obtained by actual admeasurement, furnishes a standard of measures, with which we compare the distances, masses, densities, and volumes of the sun and planets.
THE theoretical investigation of the figure of the earth and planets is so complicated, that neither the geometry of Newton nor the refined analyses of La Place have attained more than an approximation it is only within a few years that a complete and finite solution of that difficult problem has been accomplished by our distinguished coun
tryman Mr. Ivory. The investigation has been conducted by successive steps, beginning with a simple case, and then proceeding to the more difficult; but in all, the forces which occasion the revolutions of the earth and planets are omitted, because, by acting equally upon all the particles, they do not disturb their mutual relations. A fluid mass of uniform density, whose particles mutually gravitate to each other, will assume the form of a sphere when at rest; but if the sphere begins to revolve, every particle will describe a circle, having its centre in the axis of revolution; the planes of all these circles will be parallel to one another, and perpendicular to the axis, and the particles will have a tendency to fly from that axis in consequence of the centrifugal force arising from the velocity of rotation. The force of gravity is everywhere perpendicular to the surface, and tends to the interior of the fluid mass, whereas the centrifugal force acts perpendicularly to the axis of rotation, and is directed to the exterior; and as its intensity diminishes with the distance from the axis of rotation, it decreases from the equator to the poles, where it ceases. Now it is clear that these two forces are in direct opposition to each other in the equator alone, and that gravity is there diminished by the whole effect of the centrifugal force, whereas, in every other part of the
fluid, the centrifugal force is resolved into two parts, one of which, being perpendicular to the surface, diminishes the force of gravity; but the other, being at a tangent to the surface, urges the particles towards the equator, where they accumulate till their numbers compensate the diminution of gravity, which makes the mass bulge at the equator and become flattened at the poles. It appears, then, that the influence of the centrifugal force is most powerful at the equator, not only because it is actually greater there than elsewhere, but because its whole effect is employed in diminishing gravity, whereas, in every other point of the fluid mass, it is only a resolved part that is so employed. For both these reasons it gradually decreases towards the poles, where it ceases. the contrary, gravity is least at the equator, because the particles are farther from the centre of the mass, and increases towards the poles, where it is greatest. It is evident, therefore, that, as the centrifugal force is much less than the force of gravity,-gravitation, which is the difference between the two, is least at the equator, and continually increases towards the poles, where it is a maximum. On these principles Sir Isaac Newton proved that a homogeneous fluid mass in rotation assumes the form of an ellipsoid of revolution, whose compression is. Such, however, can