82 KEPLER'S PROBLEM. 



for the anomaly of the eccentric, reckoned from the aphelion 

 (16 days 4 hours and 44' from its perihelial passage), ^ is 

 173 51', and too small. The second approximation is 

 173 54' 36", exceeding the real eccentric anomaly from the 

 perihelion by only a few seconds. 



The application of the author's last correction, deduced 

 from the comparison of the parabolic and elliptic trajectories, 

 to the finding of the heliocentric place, and also the helio- 

 centric distance (or radius vector of the cometic orbit), con- 

 cludes this paper. I have been the more gratified by a 

 perusal of this last branch of Mr. Ivory's inquiry, because 

 the speculations had formerly occurred to me in a similar 

 form. The introduction of the parabola, which admits of 

 quadrature, and of definite solution, so far as regards Kepler's 

 problem, has always appeared to me the surest method of 

 rectifying the computations of the heliocentric places and 

 distances of comets, or of their perihelial eccentric anomalies 

 and radii vectores, during the small perihelial part of their 

 trajectories which we are permitted to contemplate. In that 

 part, the eccentric ellipse and the parabola nearly coincide ; 

 and, after all, we are not perfectly certain that those singular 

 bodies do not move in orbits strictly parabolic.* 



* This Paper appeared in the Second Number of the 'Edinburgh 

 Review,' January, 1803. 



