Several observers, including Huggins, Salter, and others, had previously drawn faint stars in the interior of the trapezium; but these could not be seen by Hall and Burnham in the large refractors at Washington and Chicago, and were thus proved to have no real existence. The new stars observed in the 36-inch telescope are only just within the limits of its capacity, and therefore cannot be identical with stars alleged to have been previously seen in small instruments. The fifth and sixth stars in the trapezium have been supposed to be variable, and not without reason; possibly the others are equally liable to change, but this is only conjecture. Sir J. Herschel says that to perceive the fifth and sixth stars “is one of the severest tests that can be applied to a telescope” (‘Outlines,’ 11th edit. p. 610); yet Burnham saw them both readily in a 6-inch a few minutes before sunrise on Mount Hamilton in September 1879. β and ε Lyræ also form multiple groups, which will well repay observation either with large or small telescopes. _Further Observations._—Anyone who attempts to indicate with tolerable fulness the methods and requirements of observation in the stellar department of astronomy will find a heavy task lies before him; and it is one to which he will be unable to do justice in a small space, owing to the variety of matters to be referred to and the necessity of being particular in regard to each one. In what follows I shall merely make very brief allusions, as it is hoped the description already given of past work will be a sufficient guide for the future. Moreover, those who take up a special branch of inquiry will hardly rest content with the meagre information usually conveyed in a general work on astronomy, but will consult those authorities who deal more exclusively with that branch. Double and binary stars may be said to form one department, variable and temporary stars another, the colours of stars a third, while many others may be signified—such as the determination of star-magnitudes, positions, grouping, and distances; also the proper motions and number of stars, besides photographic and spectroscopic work,—each and all of which comprise a field of useful and extensive inquiry. The amateur will of course choose his own sphere of labour, consistently with his inclination and the character of his appliances. In connection with double stars, valuable work yet remains to be done, though the Herschels and the Struves gathered in the bulk of the harvest and Burnham has gleaned much that was left. With regard to bright stars, it may be assumed that very few, if any, close companions, visible in moderately small glasses, now await discovery, unless, indeed, in cases where the star forms part of a binary system of long period, and the epoch of periastron has fallen in recent years. But with telescopic stars there must be many interesting doubles, some of them binaries, still unknown. These should be swept up and submitted