Among the circular and elliptical nebulæ a few exhibit a very remarkable structure, being apparently perforated, and forming either round, slightly oval, or elongated rings of great beauty. These Annular nebulæ are among the rarest objects in the heavens. In Scorpio, two such nebulæ are found involved in the Milky-way, and also one in Cygnus. One of those in Scorpio has two stars involved within its ring, at the extremities of its smallest interior diameter. A very elongated nebula in the vicinity of the fine triple star _γ_ Andromedæ is also annular, and has two stars symmetrically placed at the extremities of its greatest interior axis. Another elongated annular nebula is also found north of _η_ Pegasi. The grandest and most remarkable of the annular nebulæ is found in the constellation Lyra, about midway between the two stars _β_ and _γ_. It is slightly elliptical in form, and according to Prof. E. S. Holden, its major axis is 77".3 and the minor 58". From a study and several drawings which I have made of this object, with instruments of various apertures, I have found it decidedly brighter towards its outer border, at the extremities of its minor axis, than at the ends of the major axis. On very favorable occasions, some of its brightest parts have appeared decidedly, but very faintly mottled, and I have recognized three small centres of condensation. Its interior, in which Professor Holden has detected a very faint star, is quite strongly nebulous. In Lord Rosse's telescope, this nebula is completely surrounded by wisps and appendages of all sorts of forms, which I have failed to trace, however, both with the refractor of the Harvard College Observatory and with that of the Naval Observatory at Washington; Rosse, Secchi and Chacornac, have seen this nebula glittering as if it were a "heap of star dust," although its spectrum indicates that it is gaseous. The nebula No. 1,541, in Camelopardus, of which I have also made a study and a drawing, is closely allied to the class of annular nebulæ. This object, which is quite bright, has a remarkable appearance. It consists principally of somewhat more than half of an oval ring, surrounding a bright, nebulous mass which condenses around a star; this mass being separated from the imperfect ring by a dark interval. Upon the bright portion of the ring, and on opposite points, are found two bright stars, between which lies the star occupying the central mass. The central mass extends at some distance outside of the ring on its open side. Several stars are involved in this object.