The right ascension of the 17th star of Eridanus being 49° 39’ 10" and its declination 5° 55’ 25" south; and the right ascension of _b_ of Eridanus being 73° 59’ 15" and its declination 5° 25’ 10" south; I collected, that when the Comet passed the wire (or horary circle) which was October 17ᵈ 17ʰ 12’ mean time, its right ascension was 182° 34’ 0" and its declination 5° 45’ 35" south. The last time that I saw the Comet was on the 19th of October in the morning; but it then appeared so faint, that I could not observe its place. Its elongation from the sun was then but about 20 degrees; and from that day to the present it hath always been less; which is the principal reason why it was invisible to us at the time when it was in its perihelion, and hath remained so ever since. The elongation will indeed soon become greater, and yet it is probable that we shall not be able to see the Comet again; because its real distance from the sun will be greater than it was when I first saw it, and it will be also four times further from us than it was at that time. The Comet kept nearly at the same distance from the earth for ten or twelve days together after I first saw it; but its brightness gradually increased then, because it was going nearer to the sun. Afterwards, when its distance from the earth increased, altho’ it continued to approach the sun, yet its lustre never much exceeded that of stars of the second magnitude, and the tail was scarce to be discerned by the naked eye. All the forementioned observations were made with a Micrometer in a seven-foot Tube, excepting those of the 3d, 11th, and 17th days of October, which were taken with a curious Sector constructed for such purposes by the late ingenious Mr. George Graham; of which Dr. Smith has given a very exact description in his third book of Optics. Supposing the Trajectory of this Comet to be parabolic, I collected from the foregoing observations, that its motion round the sun is _direct_, and that it was in its _perihelion_ October the 21st, at 7ʰ 55’ mean (or equated) time at Greenwich. That the inclination of the plane of its Trajectory to the ecliptic is 12° 50’ 20"; the place of the descending Node ♉ 4° 12’ 50"; the place of the Perihelion ♄ 2° 58’ 0"; the distance of the Perihelion from the descending Node 88° 45’ 10"; the Logarithm of the Perihelion distance 9.528328; the Logarithm of the diurnal motion 0.667636.