These cometary appendages sometimes attain prodigious dimensions. The comets of 1680 and 1769 had tails so extended that, after their heads had set under the horizon, the extremities of these immense appendages were still seen as far up as the zenith. In a single day the tail of the comet of 1843 extended 100°, and it was thrust from the comet "as a dart of light" to the enormous distance of 48,500,000 miles, and yet of this immense appendage nothing was left on the following day. The tail of Donati's comet, in 1858, attained a real length of 42,000,000 miles, while that of the great comet of 1843 had the enormous length of 200,000,000 miles. If this last comet had occupied the position of the Sun, which it approached very nearly for a moment, the extremity of its tail would have extended 60,000,000 miles beyond the orbit of Mars. In some cases the tails of comets have been seen undulating and vibrating in a manner similar to the undulations and coruscations of light characteristic of some auroras. Many observers report having seen such phenomena. The comet of 1769 was traversed by luminous waves and pulsations, comparable to those seen in the aurora borealis. I myself observed these curious undulations in Coggia's comet in 1874, while the head of this object was below the horizon. For an hour the undulations rapidly succeeded each other, and ran along the whole length of the tail. Some of the brightest comets have shone with such splendor that they could be observed easily in full sunshine. Many comets, such as those of 1577 and 1744, have equaled Sirius and Venus in brilliancy. The great comet of 1843, which suddenly appeared in our sky, was so brilliant that it was seen by many observers at noon time, within a few degrees from the Sun. I remember that I myself saw this remarkable object in the day time, with a number of persons, who were gazing at the wonderful apparition. So brilliant was this comet, that besides its nucleus and head, a portion of its tail was also visible in the day time, provided the observer screened his eyes from the full sunlight by standing in the shadow of some building.