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but trace, with precision, the operation of his laws; use the globe he inhabits as a base wherewith to measure the magnitude and distance of the sun and planets, and make the diameter of the earth's orbit the first step of a scale by which he may ascend to the starry firmament. Such pursuits, while they ennoble the mind, at the same time inculcate humility, by showing that there is a barrier which no energy, mental or physical, can ever enable us to pass that however profoundly we may penetrate the depths of space, there still remain innumerable systems, compared with which those apparently so vast must dwindle into insignificance, or even become invisible; and that not only man, but the globe he inhabits,-nay, the whole system of which it forms so small a part,-might be annihilated, and its extinction be unperceived in the immensity of creation.
Although it must be acknowledged that a complete acquaintance with physical astronomy can be attained by those only who are well versed in the higher branches of mathematical and mechanical science, and that they alone can appreciate the extreme beauty of the results, and of the means by which these results are obtained, it is nevertheless true that a sufficient skill in analysis to follow the general outline, to see the mutual dependence of the different parts of the system, and to compre
hend by what means some of the most extraordinary conclusions have been arrived at,-is within the reach of many who shrink from the task, appalled by difficulties, which, perhaps, are not more formidable than those incident to the study of the elements of every branch of knowledge; and who possibly overrate them from disregarding the distinction between the degree of mathematical acquirement necessary for making discoveries, and that which is requisite for understanding what others have done. That the study of mathematics, and their application to astronomy, are full of interest, will be allowed by all who have devoted their time and attention to these pursuits; and they only can estimate the delight of arriving at the truths they disclose, whether it be in the discovery of a world or of a new property of numbers.
It has been proved by Newton, that a particle of matter, placed without the surface of a hollow sphere, is attracted by it in the same manner as if the mass of the hollow sphere, or the whole matter it contains, were collected in its centre. The same is, therefore, true of a solid sphere, which may be supposed to consist of an infinite number of concentric hollow spheres. This, however, is not the
Hence, by the law of action and re-action, each body is itself the centre of an attractive force extending indefinitely in space, whence proceed all the mutual disturbances which render the celestial motions so complicated, and their investigation so difficult.
The gravitation of matter, directed to a centre, and attracting directly as the mass and inversely as the square of the distance, does not belong to it when considered in mass only; particle acts on particle according to the same law when at sensible distances from each other. If the sun acted on the centre of the earth without attracting each of its particles, the tides would be very much greater than they now are; and would also, in other respects, be very different. different. The gravitation of the earth to the sun results from the gravitation of all its particles, which, in their turn, attract the sun in the ratio of their respective masses. There is a reciprocal action likewise between the earth and every particle at its surface; were this not the case, and were any portion of the earth, however small, to attract another portion, and not be itself attracted, the centre of gravity of the earth would be moved in space by this action, which is impossible.
The forms of the planets result from the reciprocal attraction of their component particles. A
detached fluid mass, if at rest, would assume the form of a sphere, from the reciprocal attraction of its particles; but if the mass revolves about an axis, it becomes flattened at the poles, and bulges at the equator, in consequence of the centrifugal force arising from the velocity of rotation,-for the centrifugal force diminishes the gravity of the particles at the equator, and equilibrium can only exist where these two forces are balanced by an increase of gravity; therefore, as the attractive force is the same in all particles at equal distances from the centre of a sphere, the equatorial particles would recede from the centre, till their increase in number balanced the centrifugal force by their attraction: consequently, the sphere would become an oblate spheroid; and a fluid partially or entirely covering a solid, as the ocean and atmosphere cover the earth, must assume that form in order to remain in equilibrio. The surface of the sea is therefore spheroidal, and the surface of the earth only deviates from that figure where it rises above, or sinks below, the level of the sea; but the deviation is so small that it is unimportant when compared with the magnitude of the earth-for the mighty chain of the Andes, and the yet more lofty Himalaya, bear about the same proportion to the earth that a grain of sand does to a globe three feet in diameter. Such is the form of the earth and
planets; but the compression or flattening at their poles is so small, that even Jupiter, whose rotation is the most rapid, and therefore the most elliptical of the planets, may, from his great distance, be regarded as spherical. Although the planets attract each other as if they were spheres, on account of their distances, yet the satellites are near enough to be sensibly affected in their motions by the forms of their primaries. The moon, for example, is so near the earth, that the reciprocal attraction between each of her particles, and each of the particles in the prominent mass at the terrestrial equator, occasions considerable disturbances in the motions of both bodies: for the action of the moon, on the matter at the earth's equator, produces a nutation in the axis of rotation, and the reaction of that matter on the moon is the cause of a corresponding nutation in the lunar orbit.
If a sphere, at rest in space, receive an impulse passing through its centre of gravity, all its parts will move with an equal velocity in a straight line; but if the impulse does not pass through the centre of gravity, its particles, having unequal velocities, will have a rotatory motion at the same time that it is translated in space. These motions are independent of one another; so that a contrary impulse, passing through its centre of gravity, will impede its progress, without interfering with its rotation.