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ALL the knowledge we possess of external objects is founded upon experience, which furnishes facts; and the comparison of these facts establishes relations, from which induction, the intuitive belief that like causes will produce like effects, leads to general laws. Thus, experience teaches that bodies fall at the surface of the earth with an accelerated velocity, and with a force proportional to their masses. By comparison, Newton proved that the force which occasions the fall of bodies at the earth's surface, is identical with that which retains the moon in her orbit:; and induction led him to conclude, that, as the moon is kept in her orbit by the attraction of the earth, so the planets might be retained in their orbits by the attraction of the sun. By such steps he was led to the discovery of one of those powers with which the Creator has ordained that matter should reciprocally act upon matter.
Physical astronomy is the science which compares and identifies the laws of motion observed on earth with the motions that take place in the heavens; and which traces, by an uninterrupted chain of deduction from the great principle that governs the universe, the revolutions and rotations of the planets, and the oscillations of the fluids at their surfaces; and which estimates the changes the system has hitherto undergone, or may hereafter expe
rience-changes which require millions of years for their accomplishment.
The accumulated efforts of astronomers, from the earliest dawn of civilization, have been necessary to establish the mechanical theory of astronomy. The courses of the planets have been observed for ages with a degree of perseverance that is astonishing, if we consider the imperfection and even the want of instruments. The real motions of the earth have been separated from the apparent motions of the planets; the laws of the planetary revolutions have been discovered; and the discovery of these laws has led to the knowledge of the gravitation of matter. On the other hand, descending from the principle of gravitation, every motion in the solar system has been so completely explained, that the account of no astronomical phenomenon can now be transmitted to posterity of which the laws have not been determined.
Science, regarded as the pursuit of truth, which can only be attained by patient and unprejudiced investigation, wherein nothing is too great to be attempted, nothing so minute as to be justly disregarded, must ever afford occupation of consummate interest and subject of elevated meditation. The contemplation of the works of creation elevates the mind to the admiration of whatever is great and noble; accomplishing the object of all study,-which, in the elegant language of Sir James Mackintosh, is to inspire the love of truth, of wisdom, of beauty, especially of goodness, the highest beauty, and of that supreme and eternal Mind, which contains all truth and wisdom, all beauty and goodness. By the love or delightful contemplation and pursuit of these transcendent aims, for their own sake only, the mind of man is raised from low and
perishable objects, and prepared for those high destinies which are appointed for all those who are capable of them."
The heavens afford the most sublime subject of study which can be derived from science. The magnitude and splendor of the objects, the inconceivable rapidity with which they move, and the enormous distances between them, impress the mind with some notion of the energy that maintains them in their motions with a durability to which we can see no limit. Equally conspicuous is the goodness of the great First Cause, in having endowed man with faculties by which he can not only appreciate the magnificence of His works, 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 enoble 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 dif ferent parts of the system, and to comprehend 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 case with a spheriod; but the celestial bodies are so nearly spherical, and at such remote distances from one
another, that they attract and are attracted as if each were a dense point situate in its centre of gravity,--a circumstance which greatly facilitates the investigation of their motions.
The attraction of the earth on bodies at its surface in that latitude the square of whose sine is, is the same as if it were a sphere; and experience shows that bodies there fall through 16:0697 feet in a second. The mean distance of the moon from the earth is about sixty times the mean radius of the earth. When the number 16.0697 is diminished in the ratio of 1 to 3600, which is the square of the moon's distance from the earth's centre, it is found to be exactly the space the moon would fall through in the first second of her descent to the earth, were she not prevented by the centrifugal force arising from the velocity with which she moves in her orbit; so that the moon is retained in her orbit by a force having the same origin, and regulated by the same law, with that which causes a stone to fall at the earth's surface. The earth may, there. fore, be regarded as the centre of a force which extends to the moon; and, as experience shows that the action and re-action of matter are equal and contrary, the moon must attract the earth with an equal and contrary force.
Newton proved that a body projected in space will move in a conic section, if it be attracted by a force directed towards a fixed point, and having an intensity inversely as the square of the distance; but that any deviation from that law will cause it to move in a curve of a different nature. Kepler ascertained, by direct observation, that the planets describe ellipses round the sun; and later observations show that comets also move in conic sections: it conse quently follows that the sun attracts all the planets and