1*14.] Lnp'erlal ifist'mte of fVance. 23S 



If an elongated eiiptical oihit may be confounded with a para- 

 bola, tlie difference is not greater between the parabola and hyper- 

 bola. The insufficiency of" the parabola in some cases has been 

 ascertained, and it has been found necessary to have recourse to the 

 elipse. Why has the necessity of the hyperbola never been Felt? 

 Of 117 comets of which we possess the elements, two only are 

 decidedly eiiptical ; the 115 others are parabolic or eiiptical. In 

 fact there is nothing to prevent us from considering these orbits as 

 hyperbolic, but difl'ering infinitely little from the parabola, and in 

 "such a case there would be no reason for being surpiised that the 

 hature of lliese orbits had escaped us. The eiiptical orbit of the 

 cbm<^t of 1 '/'>l) was only kr)own by its different returns in an interval 

 of 75 or 76 years. Had it not l)een fur that we should have re- 

 garded the orbit as parabolic. Tlie hyperbolic comets never return. 

 Hence no opportunity can ever occur of rectifying our mistake. 

 Hence we have no proof that the hyperbolic orbits arc more rare 

 thiin the eli|)tical. They may be even much more numerous with- 

 out our ever suspecting it ; but M. Laplace speaks of those only 

 whose hyperbolic orbits may be recognised by observations. ITie 

 I'act is, that we do not know one of that kind. 



Hence arises this question : What is the cause that tiie hyperbolic 

 orbits are so rare ? This problem cannot be completely solved. All 

 that we can do is to apply to it the calculus of pro'uabilities. If among 

 several different cases which a]*pear equally proliable there he one 

 which seldoin or never occurs, we seem authorised to conclude that 

 there exists a cause for its being so rare. The chances which give 

 a hyperl)ola must be very few wlien compared to the others. M. 

 Laplace finds, in fact, that we muy ivager a great many to one that 

 n nelidoslly which penetrates within the sphere of ike sun's activity, 

 so as to i)c capable of being seen, will desciive a very elongated 

 elipse or a hyperbola u'hich from the greatness of' its ox/? ivill sen- 

 sibly coincide with a parabola m the part observed. It follows from 

 the analysis of M. Laplace that in the case most favourable to 

 hyperlx)las it is 5G to 1 that the hyperbola will not be sensible. 

 Thus we might he tempted to exclude this curve, and it would be 

 so much calculation saved. In fact the hyperbola is tiever tried til! 

 both the p;irabola and elipse have failed. 



The parabola itself is only a limit, a single case between the 

 ellipse and iiyperbola, the dimensions of which may vary to in- 

 finity. Hence there is scarcely any probability of a parabolic orbit. 

 Th.' Iiyperbolas are scarcely sensible, and from exj)erience it ap- 

 pears tliat the ellipses are hardly mcjre so. The hyperbolic comets 

 nei'er return, the elliptical not till after a long interval. We have 

 no reabon to be surprized that hitherto only one has returned coOt 

 i-tatilly. 



L:i])lacc had found in the attraction of Jupiter a probable cause 

 why the comet of 1770 has not appeared eight times since that 

 period. Perhaps it is entirely evaporated, or reduced to a nucleus 

 so small and so little luniinous, that it will remain for ever invi^ 



