The light of comets sometimes fluctuates in a very extraordinary manner, and too rapidly and irregularly to be consistent with theory. In this respect, Pons’s Comet, at its last return in 1883-4 presented an eccentric behaviour. Bigourdan found that during the nineteen days from Sept. 5 to 24, 1883, the increase in the comet’s brilliancy exceeded by thirty or forty times that resulting from reflected light alone! This increase appears to have been due to a sudden outburst on Sept. 22, which occurred some time within the four hours preceding midnight. Dr. Müller, of Potsdam, witnessed a further outburst on Jan. 1, 1884, within 1-3/4 hour; and the extent of this was accurately determined by means of a photometer. He found an augmentation of seven tenths of a magnitude in the brightness of the comet, and an equally sudden fall to its previous lustre. While these fluctuations were in progress, he noticed variations in the shape of the nucleus not less remarkable than its variations in light. Those who observe future comets will do well, therefore, to be on the alert for similar phenomena. The apparent brightness of the nuclei and alterations of shape or size should be recorded on every night when observations are feasible. As a comet approaches the Sun its material apparently contracts, while with increasing distance from that luminary it expands. Usually the nucleus is extremely small and bright, and it often looks like a star shining through nebulosity. High powers must therefore be applied in its examination. Jets, aigrettes, luminous sectors, and other appendages are often involved with the nucleus and outlying coma, and they form a complicated structure well deserving further study. A good deal of mystery still surrounds these appearances; their curious forms and vagaries have yet to be explained.