field unseen, and render the work abortive. The necessary conditions of the case go far to support the view that moderate powers and fields are best; for a search, to be thorough and satisfactory, must be done critically, and with a power capable of revealing the smallest specimens of comets. _Annual Rate of Discovery._—Arranging cometary discoveries during the century from 1782 to 1881 into periods of 20 years, and comparing the annual average with that during the last eight years, we get the following numbers:— Comets Annual Period. found. average. 1782-1801 25 1·25 1802-1821 26 1·30 1822-1841 36 1·80 1842-1861 83 4·15 1862-1881 79 3·95 1882-1889 40 5·00 These discoveries seem to have been greatly accelerated about the year 1845. The yearly average between 1842 and 1881 was about 4; but between 1882 and 1889 it increased to 5, owing mainly to the diligence of Barnard and Brooks. The months in which the largest number of cometary discoveries have been effected are July and August, the figures since 1782 being— Comets Month. found. Percentage. January 22 7·6 February 20 6·9 March 18 6·2 April 25 8·7 May 17 5·9 June 21 7·3 July 34 11·8 August 38 13·2 September 22 7·6 October 20 6·9 November 26 9·0 December 26 9·0 Of 289 comets discovered during the last 108 years, 123 belonged to the first six months, while no less than 166 belonged to the last half of the year. Though comets are not confined to any special region of the heavens, there is no doubt that the vicinity of the Sun is the spot to which the comet-seeker should direct his chief attention. It is here where the majority of the discoveries have been made; and theoretically this should be so, seeing that the Sun is the controlling influence of the cometary flights, and that his position must be regarded as a sort of focus of their convergence and divergence. Hence the most likely spots are over the western horizon after sunset and the eastern horizon before sunrise. The twilight and zodiacal light, together with the mist at low altitudes, are impediments which are inseparable from this work; but they need not interfere to any serious extent if the observer is careful to make the best of his opportunities. But though special attention is recommended to the neighbourhood of the Sun, other regions should not be altogether neglected, for comets are occasionally found in nearly the opposite part of the heavens to the Sun’s place, as, for example, Zona’s Comet of November 1890. In order to save time, and to prevent troublesome references during the progress of sweeping, the brighter nebulæ should be marked upon a star-chart, so that, as they enter the field, they may be instantly identified.