appears conclusively that if such extensive and valuable results can be obtained, notwithstanding frequently bad weather, then English observers may prove equally successful, the important factor being that similar energy and ability direct their labours. _Aperture and Power required._—Opinions are divided as to the most suitable aperture and power for this work. Any telescope of from 4-to 10-inches aperture may be employed in it. A low power (30 to 50) and large field (50′ to 90′) eyepiece are imperative; and the instrument, to be really effective, should be mounted to facilitate sweeping either in a vertical or horizontal direction. A reflector on an alt-azimuth stand is a most convenient form for vertical sweeps. The defining-capacity of the telescope need not necessarily be perfect to be thoroughly serviceable, the purpose being to distinguish faint nebulous bodies, and not details of form. Far more will depend upon the observer’s aptitude and persistency than upon his instrumental means, which ought to be regarded as a mere adjunct to his powers and not a controlling influence in success, for the latter lies in himself. Very large instruments are not often used, because of their necessarily restricted fields. Moreover, a small instrument, apart from its advantage in this respect, is worked with greater facility and expedition. This is important, especially when the observer is to examine the region in the immediate neighbourhood of the Sun. He has then a very brief interval for the attainment of his purpose, and a small telescope must be used on account of its large field, its ready manipulation, and its general effectiveness on objects at low altitudes. The case is somewhat different when the search is to be conducted in regions far removed from the Sun’s place; for here the comets are in general faint, and there is time for the work to be deliberately and critically performed. Large instruments are to be recommended for these districts as capable of revealing fainter objects, though they are troublesome in several respects. They show large numbers of nebulæ, especially if the observer is exploring the region of Virgo, Coma Berenices, or Ursa Major; and he will have great difficulty in identifying them and in feeling his way with certainty. These complications are inseparable from the work, and, though chiefly affecting large apertures, should not always be shunned; for a telescope capable of displaying very faint nebulæ is also capable of showing faint comets. Many comets have eluded discovery by the inadequate reach of the instruments in the hands of comet-seekers; and the statement recently made that there are only about one hundred nebulæ liable to be mistaken for comets is not accurate, because comets in certain positions are of the last degree of faintness, and there is no identifying them from small nebulæ except by means of their motion.