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a first Approximatmi to the Orbit of a Comet, 
which that equation contains. If there were the same uncer- 
tainty in this case that both theory and experience agree in 
shewing there is in the case of the comets, the problem, as 
applied to the planets, would be a mere theoretical speculation 
without any practical utility. It may therefore be asked, what 
are the precise circumstances which make the investigation 
successful in the one case, while in the other we must seek 
aid from the nature of the orbit in order to obtain a useful 
result ? In the first place, the observations of the planets are 
susceptible of a much greater degree of accuracy than those 
of the comets ; which confines the uncertainty arising from 
the errors of observation within much narrower limits in the 
one case than in the other. In the second place, the distance 
of a planet from the sun is never equal, or very nearly equal, 
to the earth's distance from the same body ; and this occasions 
a greater curvature of the apparent path than often takes place 
with regard to the comets. We may likewise add that the 
motion of a planet, in an orbit of moderate eccentricity, is 
slower than the motion of a comet at a like distance from the 
sun ; which allows a longer interval between the observations 
of a planet, and thereby contributes to heighten the effect 
arising from the inflection of the apparent path. It is to these 
causes, as well as to the excellence of his methods of investi- 
gation, that we must ascribe the great exactness with which 
the orbits of the new planets discovered in the course of the 
present century, have been determined by M. Gauss, in a work 
of great merit, on the Theory of the Motion of the Celestial Bodies, 
published in 1809, which cannot but add much to his reputa- 
tion, already very high on account of former scientific disco- 
U 3 
veries. 
