Imperial Institute of France. 231 
with parabolas, having the same summit. The revolutions of 
such comets will be so tedious that we can scarcely expect to see or 
know them again, after the many alterations which they may have 
undergone in that part of their orbit, out of the reach of all hu- 
man view, and where so many causes may modify their elements. 
The above, if adopted, would also account for the length and 
tenuity of their tails. The nebulous matter, condensed by at- 
traction so as to form the comet, being dilated by the solar heat, 
would resume nearly its primitive tenuity, and might even eva- 
porate and be lost in space. Having thus lost its tail and its 
nebulosity, the comet will be exactly similar to the four little 
planets. It may even by being dissipated, cease to exist, and 
astronomers might lose all their labour in calculating its ele- 
ments. It would be sufficient for them to be in possession of 
the coarse approximation, which puts it in their power to satisfy 
the public curiosity, without much trouble, during the short time 
that the comet is visible from our éarth. 
Some comets, however, have exhibited peculiarities inconsist= 
ent with this hypothesis. THialley’s, for instance, has the great 
axis of its orbit smaller than that of Uranus. The comet of 1770 
had a great axis less than that of Jupiter. According to M. La- 
place, these singularities may be produced by the planetary at- 
tractions or the resistance of the ethereal medium ; but the pla- 
netary attractions ought to be very weak at the entrance of the 
comet into the sphere of the sun’s energy; and Laplace himself 
has rendered the resistance of the aérial medium very problematic 
and inconsistent with the constancy of the great axis of the pla- 
netary orbits. 
If an elongated elliptical orbit be confounded with a parabola, 
the difference is not greater between the parabola and hyperbola. 
The insufficiency of the parabola in some cases having been as- 
certained, it has been found necessary to have recourse to the 
ellipsis. How has it happened that the necessity for the hyper- 
bola has never been felt? Of 117 comets whose elements we 
are acquainted with, two only are decidedly elliptical : the re- 
mainder are parabolic or elliptical. In fact there is nothing to 
prevent us from considering these orbits as hyperbolic, but dif- 
fering infinitely little from the parabola, and in this case there 
would be no occasion for surprise at the nature of these orbits 
having escaped us. The elliptical orbit of the comet of 1759 
was only ascertained by its various returns in the interval of 75 
or 76 years, and but for these returns its orbit would have been 
regarded as parabolic. Hyperbolic comets never return; and 
hence we have no opportunity of rectifying any mistake : hence 
also we have no evidence that the hyperbolic orbits are more rare 
than the elliptical, They may be even much more numerous 
without 
