The nuclei of comets are sometimes very small, and in other cases very large. Among those which have been measured, the nucleus of the comet of 1798, I., was only 28 miles in diameter, but that of Donati's comet, in 1858, was 5,600 miles, and that of the comet of 1845 was 8,000 miles in diameter. The coma of comets is found to be even more variable than the nucleus. The changes observed in the coma are generally in close connection with those of the nucleus and tail, the same perturbations affecting simultaneously the whole comet. While the coma of the comet of 1847 was only 18,000 miles in diameter, that of Halley's comet, in 1835, was 357,000 miles, and that of the comet of 1811 was 1,125,000 miles in diameter. In general, as already stated, the coma of a comet decreases in size in approaching the Sun. That of Encke's comet, which, on October 9th, 1838, had a diameter of 281,000 miles, gradually decreased at a daily mean rate of 4,088 miles in going towards the Sun; so that, on December 17th, when the distance of the comet from the Sun was more than four times less than it was on the first date, its diameter was reduced to 3,000 miles. The form of the coma, in that part which is free from the tail, is in general a portion of a circle, but is sometimes irregular, with its border deformed. Thus, the border of the coma of Halley's comet was depressed at one point towards the Sun. I observed a similar phenomenon in Coggia's comet, with the great refractor of the Harvard College Observatory, on July 13th, 1874, when its border appeared deeply depressed on the side nearest to the Sun, as if repelled by this body. The coma of comet 1881, III., showed also very singular outlines on the nights of the 25th and 26th of June, when its border was so deeply depressed that the coma appeared as if it were double. Luminous rays and jets often radiate from the nucleus across the coma, and describe graceful lateral curves, falling backwards and gradually fading away into the tail, of which they then form a part. The rays and jets emitted by the nucleus seem at first to obey the solar attraction and travel towards the Sun; but they are soon repelled, and move backward towards the tail. It is a mystery, as yet unexplained, how these cometary jets, which at first seem to obey to the laws of attraction, are compelled to retreat apparently by superior opposing forces. Among the forces of nature, we know of no other than those of an electrical sort, which would act in a similar manner; but this explanation would require us to assume some direct electrical communication between the comet and the Sun. Considering the distance between the two bodies, and the probable absence or great tenuity of the gaseous material in interstellar space, such an assumption is a difficult one.