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Three at least the comets of 1723, 1771, and 1818 are known to have moved along hyperbolic paths instead of parabolic or elliptical ones. These comets, therefore, can make but one appearance in our skies. Having once shewn themselves there, and vanished, they are lost to us for ever.
Here is a body which comes flashing out of boundless space into our system, shooting out a pyrotechnic tail some hundreds of millions of miles in length; whirling, perhaps, through the very atmosphere of the sun at a speed of three or four hundred miles a second; then darting off on a hyperbolic orbit that forbids it ever to return, or an elliptical one that cannot be closed for hundreds or thousands of years; the tail meantime pointing always away from the sun, and fading to nothingness as the weird voyager recedes into the spatial void whence it came.
The prevalence, too, among periodical comets, of direct motion, is shown to be inevitable by M. Callandreau's demonstration that those travelling in a retrograde direction would, by planetary action, be thrown outside the probable range of terrestrial observation. The scarcity of hyperbolic comets can be similarly explained.
The Ducal Palace furnishes three anomalies in the arch, dogtooth, and dentil: it has a hyperbolic arch, as noted above, Chap.
Often it has a hyperbolic orbit, which would make it impossible to come back. Yet it may return apparently contradicting the geometry of conic sections. This only goes to prove once more that it is risky to say anything is impossible even that our hero of this story manages beautifully, with the aid of Cantrell's Comet, to avoid complete annihilation while stranded in interstellar space.
Lieutenant Procope pointed out that these curves evidently had reference to the orbits of comets, which are variously parabolic, hyperbolic, or elliptic. If either of the first two, the comet, after once appearing within the range of terrestrial vision, would vanish forever in the outlying regions of space; if the last, it would be sure, sooner or later, after some periodic interval, to return.
But whether I should ever reach the earth by that device, or whether I might not simply find myself spinning about it in some hyperbolic or parabolic curve or other, I could not tell.
He lighted a cigarette and sat at case, as though in his own study, his brow wrinkled in thought as he made calculations in his notebook. Finally he rose to his feet. "There's only one chance that I can see. That is to gather up every scrap of copper we have and try to pull ourselves far enough out of line so that we will take an hyperbolic orbit around that body instead of falling into it."
Galdan, bound by the laws of hospitality, nowhere more sacred than in the East, gave them an honorable reception, and lavished upon them the poor resources he commanded. In hyperbolic terms he declared that the arrival of an embassy from the rich and powerful Chinese emperor in his poor State would be handed down as the most glorious event of his reign.
He plunged into his speech, forgetful of what he had written, with a passion queerly hyperbolic in view of the subject. At the arresting tones of his voice many of the withdrawing members stopped at the bar and listened, then as he proceeded they gradually slipped back into their places. Curiosity gave place to interest.
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