130 Mr. Ivory on a new Method of deducing 
suppose the orbit to be a parabola : because, in this case, the 
velocity in the orbit furnishes an equation without introducing 
any new unknown quantity. Thus it happens, that in the 
problem of the comets there is one equation more than there 
are quantities sought: and by combining those equations in 
different ways, various solutions of the problem may be ob- 
tained. But it ought likewise to be observed, that if we set 
aside the equation derived from the nature of the orbit, the 
remaining ones, in the actual state of the data, will nearly 
coincide with what would result from the hypothesis of a 
uniform motion in a straight line: and although, theoreti- ^ 
cally speaking, we can solve the problem by means of those 
equations, yet we shall thus infallibly introduce coefficients 
that are small and ill defined, and unfit for any practical 
purpose. It is therefore necessary to include the velocity in 
the orbit, or some equivalent property, if we wish to obtain a 
solution useful in practical astronomy: and even when this 
mode of solution is adopted, it is still necessary to examine 
with care the quantities introduced by combining the other 
conditions, in order to exclude the faulty coefficients we have 
been speaking of. 
It is of the greater consequence to discuss the peculiarities 
of this problem, because the observations of comets are sus- 
ceptible of little accuracy even with the best instruments and 
the greatest care, on account of the haze, or coma, with which 
those bodies are generally surrounded. Every solution of a 
physical problem which is deduced from quantities that are of 
the same order as the unavoidable errors in the data furnished 
by observation, can plainly be of no practical utility ; and it is 
in this predicament that those coefficients stand, which would 
