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accelerates action alteration angle aphelion apogee appears apply approach attraction called causes the line central body centre coincide consequence consider consideration curve depending described diminished direction distance disturbing body disturbing force double draw earth effect ellipse equal equator exactly excentricity explained force acting force perpendicular former given going greater greatest inclination increased independent inequality instance irregularity Jupiter Jupiter's kind latter less line of apses line of conjunction line of nodes lite longitude manner mean distance mentioned moon moon's orbit motion moving nearly observation opposite orbit passes path perigee perihelion perijove periodic perturbation planet points position produced progress proportion radius vector reasoning regress remarkable represented respect retards revolution revolving satel Saturn second satellite seen sensibly side similar sometimes square sun's attraction suppose take place tends theory third satellite tion true turbing force variation velocity whole
29. lappuse - The third, viz. that the squares of the periodic times are proportional to the cubes of the mean distances...
22. lappuse - In all our diagrams it is to be understood, that the planet, or satellite, moves through its orbit in the direction opposite to the motion of the hands of a watch. This is the direction in which all the planets and satellites would appear to move, if viewed from any place on the north side of the planes of their orbits. The time in which the planet moves from any one point of the orbit through the whole orbit, till it comes to the same point again, is called the planet's periodic time.
14. lappuse - The planets describe ellipses which are very little flattened, and differ very little from circles. Three or four comets describe very long ellipses : and nearly all the others that have been observed are found to move in curves which cannot be distinguished from parabolas. There is reason to think that two or three comets which have been observed move in hyperbolas.
vii. lappuse - The exercise of the mind in understanding a series of propositions, where the last conclusion is geometrically in close connexion with the first cause, is very different from that which it receives from putting in play the long train of machinery in a profound analytical process. The degrees of convictiOD in the two cases are very different.
viii. lappuse - ... conclusion is geometrically in close connexion with the first cause, is very different from that which it receives from putting in play the long train of machinery in a profound analytical process. The degrees of conviction in the two cases are very different. It is known to every one who has been engaged in the instruction of students at our Universities, that the results of the differential calculus are received by many, rather with the doubts of imperfect faith than with the confidence of...
20. lappuse - A, the sun's attraction (which is always directed to the sun) retards the planet hi its orbit, just as the force of gravity retards a ball which is bowled up a hill ; and when it has reached c, its velocity is extremely small ; and, therefore, though the sun's attraction at c is small, yet the deflection which it produces in the planet's motion is, (on account of the planet's slowness there) sufficient to make its path very much curved, and the planet approaches the sun, and goes over the same orbit...
7. lappuse - The accuracy of astronomical observations is carried to a degree that can scarcely be imagined ; and by means of these we can every day compare the observed place of a planet with the place which was calculated beforehand, according to the law of gravitation. It is found that they agree so nearly as to leave no doubt of the truth of the law. The motion of Jupiter, for instance, is so perfectly calculated, that astronomers have computed ten years beforehand the time at which it will pass the meridian...
200. lappuse - Prove that the attraction of a sphere of uniform density upon an external point is the same as if all the matter of the sphere were concentrated at its centre.
5. lappuse - ... (8.) Thus, suppose that the sun and Jupiter are at equal distances from Saturn; the sun is about a thousand times as big as Jupiter; then whatever be the number of inches through which Jupiter draws Saturn in one second of time, the sun draws Saturn in the same time...