PREFACE. 



parabolic: on the contrary, it must be regarded as in the highest degree 

 improbable that nature should ever have favored such an hypothesis. Since, 

 nevertheless, it was known, that the phenomena of a heavenly body moving 

 in an ellipse or hyperbola, the major-axis of which is very great relatively to 

 the parameter, differs very little near the perihelion from the motion in a 

 parabola of which the vertex is at the same distance from the focus; and 

 that this difference becomes the more inconsiderable the greater the ratio of 

 the axis to the parameter : and since, moreover, experience had shown that 

 between the observed motion and the motion computed in the parabolic 

 orbit, there remained differences scarcely ever greater than those which might 

 safely be attributed to errors of observation (errors quite considerable in 

 most cases) : astronomers have thought proper to retain the parabola, and 

 very properly, because there are no means whatever of ascertaining satis 

 factorily what, if any, are the differences from a parabola. We must except 

 the celebrated comet of HALLEY, which, describing a very elongated ellipse and 

 frequently observed at its return to the perihelion, revealed to us its periodic 

 time ; but then the major-axis being thus known, the computation of the re 

 maining elements is to be considered as hardly more difficult than the determi 

 nation of the parabolic orbit. And we must not omit to mention that astrono 

 mers, in the case of some other comets observed for a somewhat longer time, 

 have attempted to determine the deviation from a parabola. However, all 

 the methods either proposed or used for this object, rest upon the assumption 

 that the variation from a parabola is inconsiderable, and hence in the trials 

 referred to, the parabola itself, previously computed, furnished an approximate 

 idea of the several elements (except the major-axis, or the time of revolu 

 tion depending on it), to be corrected by only slight changes. Besides, it 



