to move in circular orbits. Kepler, on the other hand, was no less in error in considering their paths to be rectilinear. James Bernoulli supposed comets to be the satellites of a very remote planet, invisible on account of its great distance,—such satellites being seen only in the parts of their orbits nearest the earth. Still more extravagant was the hypothesis of Descartes, who held that they were originally fixed stars, which, having gradually lost their light, could no longer retain their positions, but were involved in the vortices of the neighboring stars, when such as were thus brought within the sphere of the sun's illuminating power again became visible.

Comets visible in the daytime.

Comets of extraordinary brilliancy have sometimes been seen during the daytime. At least thirteen authentic instances of this phenomenon have been recorded in history. The first was the comet which appeared about the year 43 B.C., just after the assassination of Julius Cæsar. The Romans called it the Julium Sidus, and regarded it as a celestial chariot sent to convey the soul of Cæsar to the skies. It was seen two or three hours before sunset, and continued visible for eight successive days. The great comet of 1106, described as an object of terrific splendor, was seen simultaneously with the sun, and in close proximity to it. Dr. Halley supposed this and the Julian comet to have been previous visits of the great comet of 1680. In the year 1402 two comets appeared,—one about the middle of February, the other in June,—both of which were visible while the sun was above the horizon. One was of such magnitude and brilliancy that the nucleus and even the tail could be seen at midday. The comet of 1472, one of the most splendid recorded in history, was visible in full daylight, when nearest the earth, on the 21st of January. This comet, according to Laugier, moves very nearly in the plane of the ecliptic, its inclination being less than two degrees. Its least distance from our globe was only 3,300,000 miles. The comet of 1532, supposed by some to be identical with that of 1661, was also visible in full sunshine. The apparent magnitude of its nucleus was three times greater than that of Jupiter. The comet of 1577 was seen with the naked eye by Tycho Brahe before sunset. It was by observations on this body that Aristotle's doctrine in regard to the origin, nature, and distance of comets was proved to be erroneous. It was simultaneously observed by Tycho at Oranienberg, and Thaddeus Hagecius at Prague; the points of observation being more than 400 miles apart, and nearly on the same meridian. The comet was found to have no sensible diurnal parallax; in other words, its apparent place in the heavens was the same to each observer, which could not have been the case had the comet been less distant than the moon. The comet which passed its perihelion on the 8th of November, 1618, was distinctly seen by Marsilius when the sun was above the horizon. The great comet of 1744 was seen without the aid of a glass at one o'clock in the afternoon,—only five hours after its perihelion passage. The diameter of this body was nearly equal to that of Jupiter. It had six tails, the greatest length of which was about 30,000,000 miles, or nearly one-third of the distance of the earth from the sun. The spaces between the tails were as dark as the rest of the heavens, while the tails themselves were bordered with a luminous edging of great beauty.

The great comet of 1843 was distinctly visible to the naked eye, at noon, on the 28th of February. It appeared as a brilliant body, within less than two degrees from the sun. This comet passed its perihelion on the 27th of February, at which time its distance from the sun's surface was only about one-fourth of the moon's distance from the earth. This is the nearest approach to the sun ever made by any known comet. The velocity of the body in perihelion was about 1,280,000 miles an hour, or nearly nineteen times that of the earth in its orbit. The apparent length of its tail was sixty-five degrees, and its true length 150,000,000 miles. The first comet of 1847, discovered by Mr. Hind, was also seen near the sun on the day of its perihelion passage. That discovered by Klinkerfues on the 10th of June, 1853, and which passed its perihelion on the 1st of September, was seen at Olmutz in the daytime, August 31, when only twelve degrees from the sun. After passing its perihelion, it was again observed, at noon, on the 2d, 3d, and 4th of September. Finally, the great comet of 1861 was seen before sunset, on Monday evening, July 1, by Rev. Henry W. Ballantine, of Bloomington, Indiana. It was again detected on the following evening just as the sun was in the horizon.

Besides the thirteen comets which we have enumerated, at least four others have been seen in the daytime; all, however, under peculiar circumstances. Seneca relates that during a great solar eclipse, 63 years before our era, a large comet was observed not far from the sun. "Philostorgius says that on the 19th of July, A.D. 418, when the sun was eclipsed and stars were visible, a great comet, in the form of a cone, was discovered near that luminary, and was afterwards observed during the nights."[2] The comet which passed its perihelion on the 18th of November, 1826, was observed by both Gambart and Flaugergues to transit the solar disk,—the least distance of the nucleus from the sun's surface being about 2,000,000 miles. The second comet of 1819 and the comet of 1823 are both known in like manner to have passed between the sun and the earth. Unfortunately, however, the transits were not observed.

A few cometary orbits are hyperbolas, more ellipses, and a still greater number parabolas. Comets moving in ellipses remain permanently within the limits of solar influence. Others, however, visit our system but once, and then pass off to wander indefinitely in the sidereal spaces.

Comets of known periodicity.

I. Halley's Comet.

As comets are subject to great changes of appearance, one can never be identified by any description of its magnitude, brilliancy, etc., at the time of a previous return. This can be done only by a comparison of orbits. If, for example, we find the elements of an orbit very nearly corresponding in every particular with those of a former comet, there is a degree of probability, amounting almost to certainty, that the two are identical. Sir Isaac Newton, in his Principia, published shortly after the appearance of the comet of 1682, explained how the periods of those mysterious visitors might thus be ascertained, thus directing the attention of astronomers to the subject. Dr. Halley soon after undertook a thorough discussion of all the recorded cometary observations within his reach. In the course of his investigations he discovered that the path of the comet observed by Kepler in 1607 coincided almost exactly with that of the one which passed its perihelion in 1682. Hence he concluded that they were the same. He found also that the comet of 1531, whose course had been particularly observed by Apian, moved in the same path. The interval between the consecutive appearances being nearly 76 years, Halley announced this as the time of the comet's revolution, and boldly predicted its return in 1758 or 1759. The law of universal gravitation had at this time just been discovered and announced. But although its application to the determination of planetary and cometary perturbations had not been developed, Halley was