Page:Newton's Principia (1846).djvu/580

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 * style="width:95%" |The precession of the equinoxes, and the libratory motion of the axes of the earth and planet, ||535
 * That the greatest tides happen in the syzygies of the luminaries, the least in their quadratures; |and that at the third hour after the appulse of the moon to the meridian of the place. But that out of the syzygies and quadratures those greatest and least tides deviate a little from that third hour towards the third hour after the appulse of the sun to the meridian, ||536
 * That the tides are greatest when the luminaries are in their perigees, ||536
 * That the tides are greatest about the equinoxes, ||536
 * That out of the equator the tides are greater and less alternately, ||537
 * That, by the conservation of the impressed motion, the difference of the tides is diminished; and that hence it may happen that the greatest menstrual tide will be the third after the syzygy, ||538
 * That the motions of the sea may be retarded by impediments in its channels, ||538
 * That from the impediments of channels and shores various phænomena do arise, as that the sea may flow but once every day, ||539
 * That the times of the tides within the channels of rivers are more unequal than in the ocean, ||540
 * That the tides are greater in greater and deeper seas; greater on the shores of continents than at islands in the middle of the sea; and yet greater in shallow bays that open with wide inlets to the sea, ||540
 * The force of the sun to disturb the motions of the moon, computed from the foregoing principles, ||542
 * The force of the sun to move the sea computed, ||543
 * The height of the tide under the equator arising from the force of the sun computed, ||544
 * The height of the tides under the parallels arising from the sun s force computed, ||545
 * The proportion of the tides under the equator, in the syzygies and quadratures, arising from the joint forces of both sun and moon, ||545
 * The force of the moon to excite tides, and the height of the water thence arising, computed, ||545
 * That those forces of the sun and moon are scarcely sensible by any other effect beside the tides which they raise in the sea, ||546
 * That the body of the moon is about six times more dense than the body of the sun, ||547
 * That the moon is more dense than the earth in a ratio of about three to two, ||547
 * Of the distance of the fixed stars, ||547
 * That the comets, as often as they become visible to us, are nearer than Jupiter, proved from their parallax in longitude, ||548
 * The same proved from their parallax in latitude. ||549
 * The same proved otherwise by the parallax, ||550
 * From the light of the comets heads it is proved that they descend to the orbit of Saturn, ||550
 * And also below the orb of Jupiter, and sometimes below the orb of the earth, ||551
 * The same proved from the extraordinary splendor of their tails when they are near the sun, ||551
 * The same proved from the light of their heads, as being greater, cæteris paribus, when they come near to the sun, ||553
 * The same confirmed by the great number of comets seen in the region of the sun, ||555
 * This also confirmed by the greater magnitude and splendor of the tails after the conjunction of the heads with the sun than before, ||555
 * That the tails arise from the atmospheres of the comets, ||556
 * That the air and vapour in the celestial spaces is of an immense rarity; and that a small quantity of vapour may be sufficient to explain all the phænomena of the tails of comets, ||558
 * After what manner the tails of comets may arise from the atmospheres of their heads, ||559
 * That the tails do indeed arise from those atmospheres, proved from several of their phænomena, ||559
 * That comets do sometimes descend below the orbit of Mercury, proved from their tails, ||560
 * That the comets move in conic sections, having one focus in the centre of the sun, and by radii drawn to that centre do describe areas proportional to the times, ||561
 * That those conic sections are near to parabolas, proved from the velocity of the comets, ||561
 * In what space of time comets describing parabolic trajectories pass through the sphere of the orbis magnus, ||562
 * At what time comets enter into and pass out of the sphere of the orbis magnus, ||563
 * With what velocity the comets of 1680 passed through the sphere of the orbis magnus, ||564
 * That these were not two, but one and the same comet. In what orbit and with what velocity this comet was carried through the heavens described more exactly, ||564
 * With what velocity comets are carried, shewed by more examples, ||565
 * The investigation of the trajectory of comets proposed, ||566
 * Lemmas premised to the solution of the problem, ||567
 * The problem resolved, ||570
 * }
 * From the light of the comets heads it is proved that they descend to the orbit of Saturn, ||550
 * And also below the orb of Jupiter, and sometimes below the orb of the earth, ||551
 * The same proved from the extraordinary splendor of their tails when they are near the sun, ||551
 * The same proved from the light of their heads, as being greater, cæteris paribus, when they come near to the sun, ||553
 * The same confirmed by the great number of comets seen in the region of the sun, ||555
 * This also confirmed by the greater magnitude and splendor of the tails after the conjunction of the heads with the sun than before, ||555
 * That the tails arise from the atmospheres of the comets, ||556
 * That the air and vapour in the celestial spaces is of an immense rarity; and that a small quantity of vapour may be sufficient to explain all the phænomena of the tails of comets, ||558
 * After what manner the tails of comets may arise from the atmospheres of their heads, ||559
 * That the tails do indeed arise from those atmospheres, proved from several of their phænomena, ||559
 * That comets do sometimes descend below the orbit of Mercury, proved from their tails, ||560
 * That the comets move in conic sections, having one focus in the centre of the sun, and by radii drawn to that centre do describe areas proportional to the times, ||561
 * That those conic sections are near to parabolas, proved from the velocity of the comets, ||561
 * In what space of time comets describing parabolic trajectories pass through the sphere of the orbis magnus, ||562
 * At what time comets enter into and pass out of the sphere of the orbis magnus, ||563
 * With what velocity the comets of 1680 passed through the sphere of the orbis magnus, ||564
 * That these were not two, but one and the same comet. In what orbit and with what velocity this comet was carried through the heavens described more exactly, ||564
 * With what velocity comets are carried, shewed by more examples, ||565
 * The investigation of the trajectory of comets proposed, ||566
 * Lemmas premised to the solution of the problem, ||567
 * The problem resolved, ||570
 * }
 * That the comets move in conic sections, having one focus in the centre of the sun, and by radii drawn to that centre do describe areas proportional to the times, ||561
 * That those conic sections are near to parabolas, proved from the velocity of the comets, ||561
 * In what space of time comets describing parabolic trajectories pass through the sphere of the orbis magnus, ||562
 * At what time comets enter into and pass out of the sphere of the orbis magnus, ||563
 * With what velocity the comets of 1680 passed through the sphere of the orbis magnus, ||564
 * That these were not two, but one and the same comet. In what orbit and with what velocity this comet was carried through the heavens described more exactly, ||564
 * With what velocity comets are carried, shewed by more examples, ||565
 * The investigation of the trajectory of comets proposed, ||566
 * Lemmas premised to the solution of the problem, ||567
 * The problem resolved, ||570
 * }
 * That these were not two, but one and the same comet. In what orbit and with what velocity this comet was carried through the heavens described more exactly, ||564
 * With what velocity comets are carried, shewed by more examples, ||565
 * The investigation of the trajectory of comets proposed, ||566
 * Lemmas premised to the solution of the problem, ||567
 * The problem resolved, ||570
 * }
 * Lemmas premised to the solution of the problem, ||567
 * The problem resolved, ||570
 * }
 * }