There are several of Herschel's memoirs on comets. In analyzing them, we shall see that this great observer could not touch any thing without making further discoveries in the subject. Herschel applied some of his fine instruments to the study of the physical constitution of a comet discovered by Mr. Pigott, on the 28th September, 1807. The nucleus was round and well determined. Some measures taken on the day when the nucleus subtended only an angle of a single second, gave as its real angle 6/100 of the diameter of the earth. Herschel saw no phase at an epoch when only 7/10 of the nucleus could be illuminated by the sun. The nucleus then must shine by its own light. This is a legitimate inference in the opinion of every one who will allow, on one hand, that the nucleus is a solid body, and on the other, that it would have been possible to observe a phase of 8/10 on a disk whose apparent total diameter did not exceed one or two seconds of a degree. Very small stars seemed to grow much paler when they were seen through the coma or through the tail of the comet. This faintness may have only been apparent, and might arise from the circumstance of the stars being then projected on a luminous background. Such is, indeed, the explanation adopted by Herschel. A gaseous medium, capable of reflecting sufficient solar light to efface that of some stars, would appear to him to possess in each stratum a sensible quantity of matter, and to be, for that reason, a cause of real diminution of the light transmitted, though nothing reveals the existence of such a cause. This argument, offered by Herschel in favour of the system which transforms comets into self-luminous bodies, has not, as we may perceive, much force. I might venture to say as much of many other remarks by this great observer. He tells us that the comet was very visible in the telescope on the 21st of February, 1808; now, on that day, its distance from the sun amounted to 2.7 times the mean radius of the terrestrial orbit; its distance from the observer was 2.9: "What probability would there be that rays going to such distances, from the sun to the comet, could, after their reflection, be seen by an eye nearly three times more distant from the comet than from the sun?"