Whenever we look in nature we can see spiral forms in the uncurling fern, the snail, the nautilus shell, the hurricane, the stirred cup of coffee, the water that swirls out of a wash bowl. Perhaps we shouldn't be surprised to see spirals in the great star systems whirling in space. Yet they remain a great, intriguing question.
Hitherto we have considered the apparent motion of the star about its true place, as made only in a plane parallel to the ecliptic, in which case it appears to describe a circle in that plane; but since, when we judge of the place and motion of a star, we conceive it to be in the surface of a sphere, whose centre is our eye, 'twill be necessary to reduce the motion in that plane to what it would really appear on the surface of such a sphere, or (which will be equivalent) to what it would appear on a plane touching such a sphere in the star's true place.
In fact, it is safe to say that the situation has degenerated to the point of absurdity. Asteroids have been named after girlfriends, financial supporters, cats, and computers. For the traditionalist like myself, it seems a pity that the naming of asteroids has become so trivialized.
If all the potentially threatening asteroids were discovered, however, the risk to Earth would no longer be a matter of chance. We would know whether a collision is imminent. The time of impact could be predicted centuries in advance, and the place of impact could be predicted fairly accurately decades in advance.