REPORT ON ASTRONOMY. 
161 
period (1731 days) for the last comet of 1805, which it has 
since been ascertained is periodical, though with a rather longer 
time. In 1810, Bessel’s ( Untersuchungen,' §c. on the comet 
of 1807 was published : and this is an important epoch in the 
science of comets. The accuracy and long continuation of ob¬ 
servations on this comet, seemed to show clearly that an elliptic 
orbit, though of great length, must be adopted. The author 
then took into account the perturbations, by methods invented 
for that occasion and now generally adopted. He then esti¬ 
mated the greatest possible deviation which the determination 
admitted of; by giving to every observation the greatest error 
that he thought it could bear, and giving to each such a sign 
that all their effects were positive or all negative. His conclu¬ 
sion was, that after the comet had left the sensible disturbances 
of our system, its periodic time could not be less than 1404 years 
nor greater than 2157 years, and that 1543 years was most 
probable. In the Merlin Ephemeris 1815, Bessel has found a 
period of 3383 years for the great comet of 1811. Argelander 
has published a treatise on this comet; he finally hxed on 2888 
years. The most remarkable however of these long comets is 
Olbers’s of 1815. All the calculations of different observers 
agreed in giving a period of between 72 and 77 years. In a 
masterly paper printed in the Berlin Memoirs for 1813, Bessel, 
after correcting the Sun’s place, discussing all the observations, 
calculating the perturbations during and after the time of ob¬ 
servation, &c. has fixed on 1887, Feb. 9, as the time of its next 
return to perihelion. Since that time many periods have 
been found for comets, of which some have been afterwards re¬ 
jected. The second comet of 1819, as calculated by Encke, has a 
period of about 5\ years ; and the fourth comet of 1819, a period 
of 3-| years. These numbers may be correct, (though these 
bodies have not been seen again,) as many comets are so small 
that thej' can be seen only when near the earth. In the Zeit - 
schrift , vol. 2, Encke gives a period between 66 and 76 years to 
the comet of 1812, and it seems impossible that it can exceed 
100 years; in the Nachrichten , No. 22, the same writer gave 194 
years to the second comet of 1822, which he soon extended to 
1550 years ; in No. 37, Rumker fixed on 1817 years for the third 
comet of 1822 ; in No. 90, Hansen gave 556 years to the fourth 
comet of 1825: in Zach’s Correspondance i vol. 7, Mosotti thought 
that the first comet of 1822 moved in an ellipse with a period of 
three or four years, but it was finally judged to be a parabola: 
in vol. 14, a period of 265 years was given to a comet of 1825. 
The orbit of the comet of 1824 (Ast . Nach . No. 69,) appears 
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