I 
a first Approximation to the Orbit of a Comet, 131 
vanish exactly on the supposition that the earth and a comet 
moved, for a short time, with uniform velocities in straight 
lines. 
On. the whole it appears from what has been said, that the 
same circumstance to which is owing the failure of Sir Isaac 
Newton’s first method of finding a comet’s trajectory, has 
produced like effects in many of the later solutions of this 
problem. This is indeed no more than what was to be ex- 
pected : and it must excite surprise that more attention v>^as 
not paid to the peculiarities of this investigation, after Bosco- 
viCH had fully developed the solution of Newton, and shown 
the cause of its want of success. 
The English astronomer will find the methods of Boscovich 
and Laplace, properly illustrated by examples of all the 
computations, in a work published in 1793, by Sir Henry 
Englefield : in which the author has judiciously selected all 
that is practically useful from the numerous writings on this 
subject at that time before the public. 
The method of Laplace would be rigorous, were it possible 
to find exactly the numerical quantities that enter into his for- 
mulas. These are the first and second differential coefficients 
of the longitude and latitude considered as functions of the 
time ; the values of which we can do nothing more than deter- 
mine nearly by interpolating the observed places of a comet. 
With three observations only, the quantities thus found can- 
not be expected to have much accuracy, more especially if 
the motion in longitude, or latitude, be quick and irregular, as 
often happens: and when a greater number of observations is 
employed, there arises a new cause of inaccuracy in the arith- 
metical operations necessary for interpolating, which augment 
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