_Means of Measurement._—A micrometer becomes an indispensable instrument to those who make sidereal observations of an exact character. Without such means it will be impossible to determine either positions or distances except by mere estimation, and this is not sufficiently precise for double-star work. With a reliable micrometer[47] excellent results may be obtained, especially with regard to the varying angles of binary systems. Frequent remeasurement of these is desirable for comparison with the predicted places in cases where the orbits have been computed. In this department of astronomy the names of Herschel, South, Struve, Dawes, Dembowski, Burnham, and others are honourably associated, and it is notable that refracting-telescopes have accomplished nearly the whole of the work. But reflectors are little less capable, though their powers seem to have been but rarely employed in this field. Mr. Tarrant has lately secured a large number of accurate measures with a 10-inch reflector by Calver, and if care is taken to secure correct adjustment of the mirrors, there is no reason why this form of instrument should not be nearly as effective as its rival. Mr. Tarrant advises those who use reflectors in observing double stars “to test the centering of the flat at intervals during the observations, as the slightest shift of the large mirror in its cell will frequently occasion a spurious image which, if it by chance happens to fall where the companion is expected to be seen, will often lead to the conclusion that it has been observed. In addition to this, any wings or the slightest flare around a bright star will generally completely obliterate every trace of the companion, especially if close and of small magnitude, and such defects will in nine cases out of ten be found to be due to defective adjustment. Undoubtedly for very close unequal pairs the refractor possesses great advantages over a reflector of equal aperture; in the case of close double stars the components of which are nearly equal there appears to be little, if any, difference between the two classes of instruments; while for any detail connected with the colour of stars the reflector certainly comes to the fore from its being perfectly achromatic.” These remarks from a practical man will go far to negative the disparaging statements sometimes made with regard to reflectors and stellar work, and ought to encourage other amateurs possessing these instruments to take up this branch in a systematic way. _Dividing Power._—This mainly depends upon the aperture, and it was made the subject of careful investigation and experiment by Dawes, who found that the diameters of the star-disks varied inversely as the aperture of the telescope. Adopting an inch as the standard, he ascertained that this aperture divided stars of the sixth magnitude 4″·56 apart, and on this base he constructed the following table:— Aperture Least in inches. separable distance.