179 
a first Approximation to fat Orbit of a Comet, 
Place of ascend, node - 345° 6' 51" 
Place of the peri. - 149 o 28 
12. The method of finding a first approximation to a comet's 
orbit, investigated in this Paper, has now been applied to four 
examples in very different circumstances from one another; 
and the results obtained in them all are satisfactory. These 
instances will suffice for makino: the rules of calculation clear, 
and for confirming the accuracy of the analysis from which 
they have been deduced. It remains that we now consider 
the particular cases, already noticed (No. 7), in which this 
method fails. 
If a new planet should be discovered that moved exactly in 
tlic plane of the ecliptic, three geocentric observations of it 
would not be sufficient for finding its orbit. The latitudes 
being wanting in the circumstances here supposed, the longi- 
tudes alone would not furnish conditions enow for determin- 
ing the magnitude and position of the curve which the planet 
described. The same thing will likewise happen in another 
situation, when the latitudes, although not evanescent, yet 
depend, all of them in the same way, upon the longitudes ; 
and that is when the three geocentric places of the planet are 
situated in one great circle of the heavens which cuts the 
ecliptic in the points occupied by the earth and the sun at the 
time of the middle observation. This last case may indeed be 
considered as including the former one, when the plane of 
the planet's orbit coincides with the ecliptic. 
With regard to the comets it must be remembered that three 
complete observations are more than sufficient for finding an 
orbit: and on this account there are still conditions enow, but 
no more than enow, to determine the elements sought, in the 
A a 2 
