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Page 34 - ... accuracy — a striking proof of the power of analysis. A singular law obtains among the mean motions and mean longitudes of the first three satellites. It appears from observation that the mean motion of the first satellite, plus twice that of the third, is equal to three times that of the second ; and that the mean longitude of the first satellite, minus three times that of the second, plus twice that of the third, is always equal to two right angles. It is proved by theory, that if these relations...
Page 2 - The heavens afford the most sublime subject of study which can be derived from science. The magnitude and splendour 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...
Page 22 - But, in the midst of all these vicissitudes, the length of the major axes and the mean motions of the planets remain permanently independent of secular changes. They are so connected by Kepler's law, of the squares of the periodic times being proportional to the cubes of the mean distances of the planets from the sun, that one cannot vary without affecting the other.
Page 26 - That day, as other solemn days, they spent In song and dance about the sacred hill ; Mystical dance, which yonder starry sphere Of planets, and of fix'd, in all her wheels Resembles nearest, mazes intricate, Eccentric, intervolved, yet regular Then most, when most irregular they seem ; And in their motions harmony divine So smooths her charming tones, that God's own ear Listens delighted.
Page 267 - John thence concludes — 1st. That it is the heat of these rays, not their light, which operates the change ; 2ndly. That this heat possesses a peculiar chemical quality which is not possessed by the purely calorific rays outside of the visible spectrum, though far more intense ; and, 3rdly. That the heat radiated from obscurely hot iron, abounds especially in rays analogous to those of the region of the spectrum above indicated.
Page 18 - For it is clear, that if the motion be accelerated through a certain space, and then retarded through as much, the motion at the end of the time will be the same as if no change had taken place. But, as the orbits of the planets are ellipses, this symmetry does not hold : for, as the planet moves unequably in its orbit, it is in some positions more directly, and for a longer time, under the influence of the disturbing force than in others. And although multitudes of variations do compensate each...
Page 456 - These formulae, emblematic of Omniscience, condense into a few symbols the immutable laws of the universe. This mighty instrument of human power itself originates in the primitive constitution of the human mind, and rests upon a few fundamental axioms, which have eternally existed in Him who implanted them in the breast of man when He created him after His own image.
Page iii - If I have succeeded in my endeavour to make the laws by which the material world is governed, more familiar to my countrywomen, I shall have the gratification of thinking, that the gracious permission to dedicate my book to your Majesty has not been misplaced.
Page 2 - ... 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.