190 On the Great Comet of 1843. 
used by Pingré, as well as his own elements, or at least within 
such limits as those to which the errors were liable.” 
In a communication in the Inquirer of the 11th April we still re- 
peated our suggestion of the sameness of these comets. Finally in 
the Boston Courier of April 25th, Prof. Peirce published his ele- 
ments of the comet of 1689 and found an inclination smaller even 
than that of 1843, with other elements agreeing very well with 
those of the recent comet. This removed all doubt in our minds 
of the identity of these comets, and on the arrival of the London 
Times of April 14th, containing Schumacher’s opinion confirma- 
tory of Prof. Peirce’s of the sameness of the comets of 1668 and 
1843, we compared the periods to see if the comet of 1843 could 
not be both that of 1668 and 1689, and we found that: a period 
of 21% years would answer for all three. We announced this 
conclusion in a letter, dated May 8th, in the United States Ga- 
zette of May 11th, with an attempt to account for its not being 
seen except about the eighth period of its revolutions, when it 
returns to the perihelion at the same season of the year. We 
also stated that our parabolic elements, which gave an orbit pass- 
ing through our first and last normal places of March 20th and 
April 9th, gave the place on the middle date of March 30th too 
much advanced. Wealso stated that such was the case of all the 
good parabolas obtained for its orbit in Europe or America, and 
mentioned our coincidence in opinion with Encke, that the pa- 
rabola was not the true orbit, and added that probably it would 
be found to be an ellipse of 21% years. We also stated that an 
attempt further to correct the parabola for the middle observation, 
would lead to a paradox such as Encke had encountered in his 
attempt to complete an orbit on the presumption that the curve 
is a parabola. We immediately, with the kind assistance of Mr. 
John Downes, commenced the computation of an orbit on Gauss’s 
general method, without presuming upon any conic section; but 
hoping to find an ellipse, and found a double paradox, a comet 
moving in an hyperbola, and that hyperbola having its perihe- 
lion point within the body of the sun. We immediately announc- 
ed this result in the United States Gazette of the 19th April, and 
invited an expression of opinion from astronomers, as to the legit- 
imate interpretation of this result. It was manifest, that if the 
centre of gravity of the comet and tail was moving away ina 
non-periodical curve, our favorite opinion of the identity of these 
