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Consequently, anything coming to the Sun from a great distance must have one exact amount of proper motion to produce a parabola: all other amounts would give hyperbolas or ellipses. And if there are no hyperbolic orbits, then it is infinity to one that all the orbits are elliptical. This is just what they would be if comets had the genesis above supposed.
It seems to be a convention to use hyperbolic names for science-fiction magazines; a heritage from what might be called an earlier and ruder day. What I do for Astonishing is really hard work, and I enjoy it. I'm working now on one for them, based on J. W. Dunne's time-theories, if you know what they are." "I think so," Rand said. "Polydimensional time, isn't it?
That is, they will behave just as we see the majority of comets do; the orbits of which are either so eccentric as to be indistinguishable from parabolas, or else are not orbits at all, but are paths which are distinctly either parabolic or hyperbolic. In the second place, they will come from all parts of the heavens.
She would plunge into the great swelling sea of Life. She would drink sunshine and fill her soul with laughter. She would do a million hyperbolic things, the mention of which mightily confused her mother. "I, my dear," said the hen in the fairy tale, "never had the faintest desire to get into water." So, more or less, said Mrs. Oldrieve. "Will you miss me very dreadfully?" asked Zora.
The others, strapped into the control chairs, prepared themselves for the acceleration to come. If the Ancient Mariner had dropped toward the star from an infinite distance, Arcot could have applied enough power to put the ship in a hyperbolic orbit which would have carried them past the star.
His reasoning was, indeed, thereby completely vitiated, as Gauss pointed out in 1815; and the objections then urged were reiterated by Schiaparelli, who demonstrated in 1871 that a large preponderance of well-marked hyperbolic orbits should result if comets were picked up en route by a swiftly-advancing sun.
The real facts never became known, but the tales of these stirring times have been handed down in more or less hyperbolic form. It may be fairly assumed that Thomas Turnbull got reliable information from some source which he was never known to disclose, and having got it, he hastened to use it judiciously and to advantage.
Now there is nothing to hinder us from admitting these ideas to possess an objective and hyperbolic existence, except the cosmological ideas, which lead reason into an antinomy: the psychological and theological ideas are not antinomial.
In considering them, as we have done, as minute nebulosities, wandering from solar system to solar system, and formed by the condensation of the nebulous matter everywhere existent in profusion in the universe, we see that when they come into that part of the heavens where the sun is all-powerful, he forces them to describe orbits either elliptical or hyperbolic, their paths being equally possible in all directions, and at all inclinations of the ecliptic, conformably to what has been observed.
The maltster's lack of teeth appeared not to sensibly diminish his powers as a mill. He had been without them for so many years that toothlessness was felt less to be a defect than hard gums an acquisition. Indeed, he seemed to approach the grave as a hyperbolic curve approaches a straight line less directly as he got nearer, till it was doubtful if he would ever reach it at all.
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