It seems impossible to doubt that some tails of comets are hollow cylinders or hollow cones. Such a theory would account for the fact, so often noticed, that single tails are usually much brighter at their two edges than at the centre. This is the natural effect of looking transversely at any translucent cylinder of measureable thickness. It was long a moot point whether comets are self-luminous, or whether they shine by reflected light; but it is now generally admitted that whilst a part of the light of a comet may be derived by reflection from the Sun yet as a rule they must be regarded as shining by their own intrinsic light. It should be stated here by way of caution that the observations on this subject are not so consistent as one could wish, and it seems necessary to assume that all comets are not constituted alike, and that therefore what is true of one does not necessarily apply to another. To those who possess telescopes (not necessarily large ones) opportunities for the study of comets have much multiplied during the last few years, for we are now acquainted with a group of small comets which are constantly coming into view at short intervals of time. The comets have now become so numerous that seldom a year passes without one or more of them coming into view. Whilst that known as Encke’s revolves round the Sun in 3¼ years, Tuttle’s doing the same in 13½ years, there are four others whose periods average about 5½ years, 5 which average 6½ years, together with one of 7½ years and one of 8 years. It is thus evident that there is a constant succession of these objects available for study, and that very few months can ever elapse that some one or more of them are not on view. They bear the names of the astronomers who either discovered them originally, or who, by studying their orbits, discovered their periodicity. The names run as follows, beginning with the shortest in period and ending with the longest:— Encke’s. Winnecke’s. Temple’s Second (1873, II.) Brorsen’s. Temple’s First (1867, II.) Swift’s (1880, V.) Wolf’s (1884, III.) Barnard’s (1884, II.) Faye’s. D’Arrest’s. Denning’s. Finlay’s. Tuttle’s. I cannot stay to dwell upon either the history or description of these comets separately, but must content myself by saying generally that whilst as a rule they are not visible to the naked eye, yet several of them may occasionally become so visible when they return to perihelion under circumstances which bring them more near than usual to the earth. Several other comets are on record which it was supposed at one time would certainly have been entitled to a place in the above list, but three of them in particular have, under very mysterious circumstances, entirely disappeared from the Heavens.