200 On the Great Comet of 1843. 
* 
of the eccentricity of the densest portion of the nebulosity in that 
nebulosity. It confirms the remark, we published in the United 
States Gazette of April 6th. It confirms the coincident opinions 
of Profs. Alexander and Bartlett. It explains away the seeming 
paradoxes of the hyperbolic motion of the apparent centre of the 
nebulosity, and of the tendency of this fictitious curve to a peri- 
helion point within the sun’s surface, while the true ellipse of 
21% years’ period has a perihelion distance greater than the sun’s 
radius, leaving the comet free to depart and return, as it must do 
about the Ist of January, 1865, to be seen under more favorable 
circumstances than at this visit. 
We conclude by expressing our great satisfaction at the expla- 
nation of Profs. Alexander and Bartlett, which, with the computa- 
tions of the new orbit, by Henderson, for the comet of 1668, and 
by Prof. Peirce for 1689, have removed the only known obstacle 
to the admission of the period of 21% years and the elliptic orbit 
suggested ‘by ourselves on the 8th inst. ; accordingly we offer it 
to the members of the Society on this their centennial celebra- 
tion, as the established period of this remarkable comet. 
Encke in 1819, from 21 days’ observation of his comet, found 
by the application of Gauss’s method, a mean daily motion of 
989’.3, whereas the true motion was 1076”.9. - In 1826 Santini 
found from 30 days’ observations of Gambart’s comet, a mean 
daily motion of 700.4, whereas the true motion was 528”.0. Our 
mean motions from the elements and the true period are respect- 
ively 159”.6 and 162.2. The conjectures of Encke and Santini 
turned out to be true. Our coincidence is even closer; but re- 
quires an additional hypothesis, that of Messrs. Herrick, Alexan- 
der, and Bartlett, which in some degree weakens the inference. 
If we admit this hypothesis, and suppose that the perihelion 
distance was possible, that is, for instance, greater than 0.0047, 
then we shall find the elliptic elements of the comet’s orbit the 
same as the hyperbolic, omitting the Gaussian angle, and making 
the eccentricity greater than 0.9994. 
The actual elliptic elements may be found on this hypothesis 
by assuming the above value of 0.9994 for the elliptic eccentri- 
city, and then giving to the difference between the elliptic and 
hyperbolic radii vectores the form of a constant quantity multi- 
plied by the reciprocal of the square of the elliptic radius vector. 
This constant should then be determined from the series of obser- 
