i«9 
a first Approximation to the Orbit of a Comet, 
observation, and it cannot be entirely obviated merely by 
pursuing new methods of solution, nor by pushing calculation 
to greater degrees of exactness. The problem cannot be 
justly and usefully solved, unless such coefficients are ex- 
cluded, and the result is obtained by means of quantities on 
which the errors of observation have no more influence than 
they ought to have. 
There are however some solutions of this problem to which 
the preceding observations must not be applied. Of this kind is 
the method of M. Boscovich ; that of the celebrated Laplace f 
and those which Legendre has more lately published :*f all 
of which have been founi useful in practical astronomy. The 
method of Boscovich owes its utility as an approximation to 
the circumstance of introducing the velocity in the orbit as a 
^principal condition: for that velocity depending upon the pro- 
jportion of the distances of the earth and the comet from the 
•sun, /limits the other conditions, and places the orbit in its pro- 
‘per situation. The same thing may be said of the methods of 
•Laplace and Legendre : and, in general, we -may affirm that 
no solution of this problem can be free from the imperfections 
we have pointed out, in which the velocity in the orbit, or 
some equivalent property, does not enter as a principal con- 
.dition. 
'In order to place what has been said in a clearer light, it is 
■to be observed that three complete observations of a celestial 
,body are sufficient for determining the species, the magnitude, 
•and the position of the curve in which it moves round the sun. 
:On this account there is a superfluity of conditions when we 
• Mec. Celeste, Tom. i. Liv. z, chap. 4. 
.Nouvelles Methodes pour la Determination des Orbites des Cometes, i8c6. 
MDCCCXIV. S 
