Page:The story of the comets.djvu/225

XI. comet relative to the Sun at the beginning of time. But the instant a third body is added to the system this is no longer true. The parabola is a limiting curve, is what might be called a curve of 'unstable' motion. To describe a parabola about the Sun, a body must have at each point of its path a certain definite velocity. If this parabolic velocity be changed by the slightest amount, the path ceases at once to be a parabola; if through any cause the velocity be decreased the path becomes an ellipse; if increased, an hyperbola. Now if a comet start in a parabolic orbit, it cannot continue for a single instant in that path, for it must of necessity be attracted by Jupiter, by Saturn, or by some or all of the planets, and such attraction will either increase or decrease its speed. Thus a parabolic orbit is a physical impossibility.

"Yet to-day the greater number of newly discovered comets are classed as parabolic, and their orbits are computed and given as parabolas. This is because a very small part of the actual orbit is seen, such a small part that it is impossible to determine the exact character of the real path. Near perihelion the difference between an elliptic orbit of great eccentricity and a parabolic orbit is so slight as to be inappreciable. On the other hand, the labour of keeping track of a body moving in a very eccentric elliptic orbit is many, many times greater than that required to keep track of a body moving in the corresponding parabola. Parabolic orbits are thus computer's fictions, approximate paths assumed for the purpose of lessening labour."

An exemplification of some of the uses of logarithms in connection with the orbits of elliptic comets may here be given, because some computers in publishing the results of