This comet was first detected on 1668 March 3.8 at the Cape of Good Hope in South Africa. No details were provided, but later orbits indicated the comet was then in Cetus and it was probable that only the tail was seen. The comet had passed only 1.5° from the sun on February 29. An independent discovery was made by an anonymous writer in Lisbon, Portugal on March 5. That author wrote, "The Body thereof is not seen, because it remains hid in the Horizon. Its train is of a stupendious length, extended in appearance over almost the 4th part of the visible Heaven, from West to East; its apparent breadth is of a good Palm, and its splendor very great, but it lasts but a few hours." Also, on the 5th, an observer in Goa, India, detected the tail of the comet, with the head still below the horizon. A further independent discovery was made on March 5.9, when Father Valentine Estancel (a Jesuit living in Brazil) observed the comet "a little above the horizon from west to east-southeast." It exhibited extraordinary brightness and displayed a tail 23° in length. He added, "The Globe or Head of it was so small and thin, that very few could discern it with the naked eye...." Estancel said a telescope allowed him to see the head well.
The comet reached its most southerly declination of -11.0° (apparent) on March 6. By the 7th it was observed in China as "a stretch of white light" towards the southwest. It was described as over 6° long and pointing southeastward. Estancel said the comet had slightly faded by the 6th "and become so thin, that the eye could easily see the stars that were behind it," and on the 8th he said even more stars could be seen through the comet.
Giovanni Domenico Cassini (Bologna, Italy) obtained his first observation on the 10th during the first hour of the night and saw a "path of light" which he presumed was a comet, extending from Cetus through Eridanus. The tip of the tail lay near 14 Eridani, while the head was either hidden by "horizontal clouds" or still below the horizon. By the second hour of the night, Cassini said the comet was "demersed in the mists of the horizon." Cassini's horizon was overcast in the west as night began on the 11th, but after the first hour of night he saw "a brightness in the Whale [Cetus], at least for half an hour, which was very like the splendour of Venus, likewise veiled by thin clouds." By the 12th Cassini said the tail was "more northerly than the day before yesterday, and more easterly...." It extended away from the sun and was about 32° long.
The comet entered Eridanus on March 17 and the increasing distances from the sun and Earth were taking a toll on the brightness. The Chinese saw the comet on the 18th and said the tail was over 40° long. The comet was faintly seen by an observer in Goa on the 21st, which marked the final time a position was obtained. Moonlight began causing problems thereafter and the comet was last detected on March 30.5 by the Chinese. Estancel summarized his observations by saying, "...it was at first very splendid, and cast it self with the vividness upon the Sea, that the Rays thereof were reverberated unto the shore, where the Observers stood. But this brightness lasted only for three days, after which it did considerably decay. But that which seem'd somewhat strange, was, that having lost so much of its light, yet its bulk was not diminisht but continued rather increasing until the Comet dis-appeared."
Astronomers apparently considered the available positions too rough for reliable orbital computations, but, finally, in 1843 attempts were made. Thomas Henderson became the first person to try computing an orbit for this comet and he documented his attempts in two papers published in the Astronomische Nachrichten during April and July 1843. Henderson worked with a map drawn by an observer in Goa. The map contained 13 positions obtained during the period of March 9 to 21. Although his first paper contained a rather non-sungrazer orbit with a perihelion distance of 0.25 AU and an inclination of 27°, the paper ended with another orbit with a perihelion date of 1668 March 1.3, a perihelion distance of 0.0048 AU, and an inclination of 144°, which was very similar to that expected for a sungrazer. Henderson explored the matter in his July paper. He took the orbit of the sungrazer C/1843 D1 and applied it to the observations obtained for the 1668 comet. He said it allowed a good fit to the observations. He suggested, "This comparison and the great similarity in the appearances of the comets seem to render it very probable that the comets are the same. However the agreement within tolerable limits of the observed and computed places in 1668 is not sufficient of itself to establish the identity; as orbits widely different may be found to represent the rough observations made at that period." Thus, Henderson was on the right track, but instead of discovering a comet family, he was leaning towards the theory that the two comets were the same.
Kreutz had an advantage when he wrote his paper which presented evidence for a family of sungrazing comets in 1901. A further well-observed comet seen in 1882 had a similar orbit to that of the comet of 1843, but plainly moved in an orbit with a period of several hundred years. In additions, there were two other lesser observed comets seen in 1880 and 1887 which moved in similar orbits. Thus, these comets could not have been one and the same. Kreutz suggested a family of comets was responsible and attempted to look for further candidates. Upon examining the comet of 1668 he said a parabolic orbit computed using observations obtained during the period of March 5 to 21 indicated a perihelion date of February 28.08 and a perihelion distance of 0.067 AU. He said a sungrazing orbit did not fit the rough observations as well, but indicated the comet passed perihelion on March 1.4.