October 7d 16h 54' the 79th Leonis in the British Catalogue (whose right ascension was 167° 53' 37" and declination 2° 44' 15" north) followed the Comet 13' 0" in right ascension, and was more northerly 38' 35". Hence the Comet's right ascension was 167° 40' 37" and its declination 2° 5' 40" north.
October 8d 16h 53' the Comet preceded v Leonis 1° 53' 30" in right ascension, and was 37' 20" more northerly. The right ascension of this star was 171° 7' 45" and its declination 0° 30' 55" north; therefore the Comet's right ascension was 169° 14' 15" and its declination 1° 8' 15" north.
October 11d 16h 52' the Comet followed v Leonis 2° 33' 30" in right ascension, and appeared 1° 55' 5" more southerly; but it being near the horizon, the difference of right ascension must have been contracted by refraction about 1' 5", and the difference of declination about 1' 30": so that the corrected right ascension of the Comet was 173° 42' 20" and its declination 1° 25' 40" south.
Immediately after this observation a fog arose, which prevented me from repeating it; and several mornings following proving hazy or cloudy, I could not see the Comet again till October 18th, about an hour and a quarter before sun-rising; when the twilight being strong, and the Comet low, it appeared very faint. However, I was unwilling to omit the opportunity of determining its place, as near as I could, by a single observation, in the following manner.
At 6h 59' 54" ½ sidereal time, I observed the passage of the Comet over the perpendicular wire of my equatorial Sector; then leaving the instrument in the same position till the next evening, I observed, that at 22h 8' 15" sidereal time, the 17th star of Eridanus in the British Catalogue passed over the same wire (or horary circle) 9' 30" more southerly than the Comet. And at 23h 45' 36" sidereal time the star marked b in Eridanus passed, 19' 55" more northerly than the Comet.
I found that the situation of my instrument was not sensibly altered between the 18th and 19th of October; for the transits and the difference of declination of the same stars being observed with it again on the 19th of October, they agreed very well with those that were taken the preceding night. It may therefore be supposed, that the position of the instrument continued the same likewise during the time of the foregoing observations.
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.