a parabola on the other, according to the amount of the obliquity. When a cone is cut in a direction so that the inclination of the cutting plane to the axis of the cone is less than the constant angle formed by the generating line of the cone and the axis, as E F, the resulting section will be a Hyperbola. When a cone is cut in a direction so that the inclination of the cutting plane to the axis of the cone is equal to the constant angle formed by the generating

Fig. 93.

DIAGRAM OF A PARABOLIC AND AN ELLIPTIC ORBIT.

line of the cone and the axis, as G H, the resulting section will be a Parabola.

It will be evident from an inspection of the diagram that no comet can be periodical which does not come to us following an elliptic path. In consequence, however, of the comparative facility with which a parabola can be calculated, astronomers are in the habit of seeking to apply that curve to represent the orbit of any newly discovered body. Parabolic elements having been obtained, a search is then made through a catalogue of comets whose orbits have already been calculated, to see whether the new elements resemble