the earth upon its axis. Besides this apparent motion, it has a real and proper motion of its own, by which it is continually shifting its place in the heavens, in conformity to the nature of the orbit in which it moves. "The proper course of a comet may be found by observing every night its distances from two fixed stars whose longitudes and latitudes are known; or by finding its altitude when in the same azimuth with two known fixed stars; or by noting four fixed stars in the point of intersection of the two lines connecting which the comet is found. If the places of the comet, as thus observed every night, be marked on the celestial globe, a line drawn through them will represent the comet's path among the stars; a great circle drawn through three distant places will nearly show the way it has to go. If it be continued till it intersect the ecliptic, it will show nearly the place of the node and the inclination of the orbit to the ecliptic."* There is, however, a practical difficulty which perplexes the observer in attempting to ascertain the true form of a cometary orbit. A comet remains so short a time in sight, and describes so small a part of its course within our view, that, from observation alone, without the assistance of hypothesis, we should not be able to determine the nature of its path. The only part of the course of a comet that can ever be visible is a portion throughout which the ellipse, the parabola, and hyperbola, so closely resemble each other that no observations can be obtained with sufficient accuracy to enable us to distinguish them. The hypothesis most conformable to analogy is, that the comet moves in an ellipse, having the sun in one of the foci, and that the radius vector from the sun to the comet describes areas proportional to the times, according to the law observed by the planets. If it be supposed that the comet describes an ellipse or a parabola, in conformity to the laws of Kepler, then from three geocentric places, known by observation, the orbit may be determined. The orbits of the planets, although elliptical, approach very nearly to circles; but those of comets are extremely eccentric, and form very elongated ellipses. The orbit of Halley's comet is four times longer than it is broad, and the orbits of those comets whose periodical revolution exceeds a hundred or a thousand years must be still more elongated and eccentric. The following figure represents the orbit of Hal * Dr. O. Gregory's "Treatise on Astronomy." |