Last Thursday evening, the 15th of December, about half after eight o'clock, while I was taken up with observing Saturn, my sister looked over the heavens, and discovered a pretty large, telescopic comet, in the breast of Lacerta. I viewed it in my seven-feet reflector, and with that instrument settled its place and rate of moving. At 9 h 42' 4",8 true mean time, it preceded a small telescopic star 11",3 in time, and was 2' 41" south of the same. The place of this star I have since determined with sufficient accuracy, that it may be found again by those who wish to settle it more exactly. It follows the 2d of Flamsteed's stars in the constellation of Lacerta, 1' 41",5 in time; and is 45' 40",8 more south than the same. The apparent motion of the comet on Thursday evening was direct, and at the rate of about three minutes of time in right ascension, and a little more than two degrees in polar distance per day; from which we may suppose that we shall keep it some time in view. Last night I. examined it with a twenty-feet reflector, and found it to consist of a great light, pretty regularly scattered about a condensed small part of five or six seconds in diameter; which resembled a kind of nucleus, but had not the least appearance of a solid body. Beside the scattered, and gradually diminishing light, which reached nearly to a distance of three minutes every way beyond the bright centre, there was also a faintly extended, ill defined, pretty broad ray, of about 15 minutes in length, directed towards the north following part of the heaven, which might be called the tail of the comet. Its place for the same night (Dec. 16th) was determined by a five-feet Newtonian Sweeper , carrying an equilateral triangle in the focus of the eye-glass, not so large but that the three intersections, made by the wires at the three angles, may be distinctly perceived. At 5 h 49' 40'',6 it preceded the 6th Lacerta 4' 5 8" ,5 in time, and was 5 2' 14",5 more north than that star.