SH 

 it n 



PERIODIC COMETS. 



comets were regarded before the theory of gravitation had been 

 yet firmly established or generally accepted, and while it was, so 

 to speak, upon its trial. These bodies were, in fact, looked for as 

 the witnesses whose testimony must decide its fate. 



14. Difficulties, however, which seemed almost insurmountable, 

 opposed themselves to a satisfactory and conclusive analysis of 

 their motions. Many causes rendered the observations upon their 

 apparent places few in number and deficient in precision. The 

 arcs fj a g, g' a y', and g" a g" of the three classes of orbit in 

 any of which they might move without any violation of the law 

 of gravitation were very nearly coincident in the neighbourhood 

 of the place of perihelion a. It was, for example, in almost all 

 the cases which presented themselves, possible to conceive three 

 different curves, an eccentric ellipse, such as a b a' b', a parabola, 

 such as p' p a, and an hyperbola, such as h f h a, so related that 

 the arcs gag, g' a g', and g" a g", would not deviate one from 

 another to an extent exceeding the errors inevitable in cometary 

 observations. Thus any one of the three curves within the limits of 

 the visible path of the comet might with equal fidelity represent 

 its course. In such cases, therefore, it was impossible to infer, 

 from the observations alone, whether the comet belonged to the 

 class of hyperbolic or parabolic bodies, which have no periodic 

 character, or to the elliptic, which has. 



15. The character of periodicity itself, which belongs exclusively 

 to elliptic orbits, supplied the means of surmounting this diffi- 

 culty. If any observed comet have an elliptic motion, it must 

 return to perihelion after completing its revolution, and it must 

 have been visible on former returns to that position. Not only 

 ought it to be expected, therefore, that such a comet would re- 

 appear in future after absences of equal duration (depending on 

 its periodic time), but that its previous returns to perihelion 

 would be found by searching among the recorded appearances of 

 such objects for any, the dates of whose appearance might cor- 

 respond with the supposed period, and whose apparent motions, if 

 observed, might indicate a real motion in an orbit, identical or 

 nearly so with that of the comet in question. 



If the motion of such a body were not affected by any other 

 force except the solar attraction, it would re-appear after each 

 successive revolution at exactly the same point; would follow, 

 while visible, exactly the same arc g" a g" ; would move in the 

 same plane, inclined at the same angle to the ecliptic, the nodes- 

 retaining the same places ; and would arrive at its perihelion at 

 exactly the same point a, and after exactly equal intervals. 



Now, although the disturbing actions of the planets near which 

 it might pass, in departing from and returning to the sun, must 



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