Any section, _EF_, of this cone, whose plane makes with the axis an angle equal to _NOP_, is a _parabola_. It will be seen, that, by changing the obliquity of the plane _CD_ to the axis _NO_, we may pass uninterruptedly from the circle through ellipses of greater and greater elongation to the parabola. Any section, _GH_, of this cone, whose plane makes with the axis _ON_ an angle less than _NOP_, is a _hyperbola_. [Illustration: Fig. 59.] It will be seen from Fig. 59, in which comparative views of the four conic sections are given, that the circle and the ellipse are _closed_ curves, or curves which return into themselves. The parabola and the hyperbola are, on the contrary, _open_ curves, or curves which do not return into themselves. 49. _A Revolving Body is continually Falling towards its Centre of Revolution._--In Fig. 60 let _M_ represent the moon, and _E_ the earth around which the moon is revolving in the direction _MN_. It will be seen that the moon, in moving from M to N, falls towards the earth a distance equal to _mN_. It is kept from falling into the earth by its orbital motion. [Illustration: Fig. 60.] The fact that a body might be projected forward fast enough to keep it from falling into the earth is evident from Fig. 61. _AB_ represents the level surface of the ocean, _C_ a mountain from the summit of which a cannon-ball is supposed to be fired in the direction _CE_. _AD_ is a line parallel with _CE_; _DB_ is a line equal to the distance between the two parallel lines _AD_ and _CE_. This distance is equal to that over which gravity would pull a ball towards the centre of the earth in a minute. No matter, then, with what velocity the ball _C_ is fired, at the end of a minute it will be somewhere on the line _AD_. Suppose it were fired fast enough to reach the point _D_ in a minute: it would be on the line _AD_ at the end of the minute, but still just as far from the surface of the water as when it started. It will be seen, that, although it has all the while been falling towards the earth, it has all the while kept at exactly the same distance from the surface. The same thing would of course be true during each succeeding minute, till the ball came round to _C_ again, and the ball would continue to revolve in a circle around the earth. [Illustration: Fig. 61.] 50. _The Form of a Body's Orbit depends upon the Rate of its Forward Motion._--If the ball _C_ were fired fast enough to reach the line _AD_ beyond the point _D_, it would be farther from the surface at the end of the second than when it started. Its orbit would no longer be circular, but _elliptical_. If the speed of projection were gradually augmented, the orbit would become a more and more elongated ellipse. At a certain rate of projection, the orbit would become a _parabola_; at a still greater rate, a _hyperbola_.