_Dec. 21st, 1788._—About 8 o’clock I viewed the comet which my sister had a little while before pointed out to me with her small Newtonian _sweeper_. In my instrument, which was a ten-foot reflector, it had the appearance of a considerably bright nebula, of an irregular round form, very gradually brighter in the middle, and about five or six minutes in diameter. The situation was low, and not very proper for instruments with high powers. _Dec. 22nd._—About half-after 5 o’clock in the morning I viewed it again, and perceived that it had moved apparently in a direction towards δ Lyræ, or thereabout. I had been engaged all night with the twenty-foot instrument, so that there had been no leisure to prepare my apparatus for taking the place of the comet; but in the evening of the same day I took its situation three times.... In every observation I found the small star which accompanies β Lyræ exactly in the parallel of the comet. These transits were taken with a ten-foot reflector, and the difference in right ascension, I should suppose, may be depended upon to within a second of time. The determination also of the parallel can hardly err so much as 15 seconds of a degree. This, and several evenings afterwards, I viewed the comet again with such powers as its diluted light would permit, but could not perceive any sort of nucleus which, had it been a single second in diameter, I think, could not well have escaped me. This circumstance seems to be of some consequence to those who turn their thoughts on the investigation of the nature of comets, especially as I have also formerly made the same remark on one of the comets discovered by Mr. Mechain in 1787, a former one of my sister’s in 1786, and one of Mr. Pigott’s in 1783 in neither of which any defined, solid nucleus, could be perceived. I have the honour to remain, Sir, &c., WM. HERSCHEL. SLOUGH, NEAR WINDSOR, _March 3, 1789_. The third comet was discovered on the 7th January, 1790; the fourth on the 17th April of the same year, during her brother’s absence from home. It was announced to Sir Joseph Banks in the following letter:— _April 19th, 1790._ SIR,— I am very unwilling to trouble you with incomplete observations, and for that reason did not acquaint you yesterday with the discovery of a comet. I wrote an account of it to Dr. Maskelyne and Mr. Aubert, in hopes that either of those gentlemen, or my brother, whom I expect every day to return, would have furnished me with the means of pointing it out in a proper manner.