COMETS. 



distance, without ever reuniting, but assuming directions when* 

 the distance from the focus bears a high ratio to the peri- 

 helion distance, which are practically undistinguishable from 

 parallelism. 



One parabolic orbit differs from another in its perihelion dis- 

 tance. The less this distance is, the less will be the separation at 

 a given distance from s between the parallel directions to which 

 the indefinite branches p p' tend. This distance may have any 

 magnitude. The body in its perihelion may graze the surface of 

 the sun, or may pass at a distance from it greater than that of the 

 most remote of the planets, so that, although it be subject to solar 

 attraction, it would in that case never enter within the limits of 

 the solar system at all. 



A body moving in such an orbit, therefore, would not make, 

 like one which moves in an ellipse, a succession of revolutions- 

 round the sun ; nor can the term periodic time be applied at all 

 to its motion. It enters the system in some definite direction, 

 such asp' p, as indicated by the arrow from an indefinite distance. 

 Arriving within the sensible influence of solar gravitation, the 

 effects of this attraction are manifested in the curvation of its path, 

 which gradually increases as its distance from the sun decreases, 

 until it arrives at perihelion, where the attractive force, and con- 

 sequently the curvature, attain their maxima. The extreme 

 velocity which the body attains at this point produces, in virtue- 

 of the inertia of the moving mass, a centrifugal force, which 

 counteracts the gravitation, and the body, after passing perihelion, 

 begins to retreat ; the solar gravitation and the curvature of its- 

 path decreasing together, until it issues from the system in a 

 direction p p' t as indicated by the arrows, which is nearly a straight 

 line, and parallel to that in which it entered. In such an orbit a 

 body therefore visits the system but once. It enters in a certain 

 Direction from an indefinite distance, and, passing through its 

 perihelion, issues in a parallel direction, passing to an unlimited 

 distance, never to return. 



7. Hyperbolic orbits, like the parabolas, consist of two inde- 

 finite branches, which unite at perihelion, which at equal dis- 

 tances from perihelion have equal curvatures, and which, as the 

 distance from perihelion increases, approach indefinitely in direc- 

 tion and form to straight lines, but, unlike the parabolic orbits, 

 the straight lines to whose direction the two branches approximate 

 are divergent and not parallel. 



Such an orbit having the same perihelion distance as the ellipse 

 and parabola, is represented by a h h', fig. 1. 



The parabola is included between the ellipse and hyperbola. 



8. When the theory of gravitation was first propounded by its. 

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