We may at once relinquish any hope of identification from drawings of the object, but, fortunately, there is one feature of a comet on which we can seize, and which no fluctuations of the actual structure can modify or disguise. The path in which the body travels through space is independent of the bodily changes in its structure. The shape of that path and its position depend entirely upon those other bodies of the solar system which are specially involved in the theory of Encke's comet. In Fig. 70 we show the orbits of three of the planets. They have been chosen with such proportions as shall make the innermost represent the orbit of Mercury; the next is the orbit of the earth, while the outermost is the orbit of Jupiter. Besides these three we perceive in the figure a much more elliptical path, representing the orbit of Encke's comet, projected down on the plane of the earth's motion. The sun is situated at the focus of the ellipse. The comet is constrained to revolve in this curve by the attraction of the sun, and it requires a little more than three years to accomplish a complete revolution. It passes close to the sun at perihelion, at a point inside the path of Mercury, while at its greatest distance it approaches the path of Jupiter. This elliptic orbit is mainly determined by the attraction of the sun. Whether the comet weighed an ounce, a ton, a thousand tons, or a million tons, whether it was a few miles, or many thousands of miles in diameter, the orbit would still be the same. It is by the shape of this ellipse, by its actual size, and by the position in which it lies, that we identify the comet. It had been observed in 1786, 1795, and 1805, but on these occasions it had not been noticed that the comet's path deviated from the parabola. Encke's comet is usually so faint that even the most powerful telescope in the world would not show a trace of it. After one of its periodical visits, the body withdraws until it recedes to the outermost part of its path, then it will turn, and again approach the sun. It would seem that it becomes invigorated by the sun's rays, and commences to dilate under their genial influence. While moving in this part of its path the comet lessens its distance from the earth. It daily increases in splendour, until at length, partly by the intrinsic increase in brightness and partly by the decrease in distance from the earth, it comes within the range of our telescopes. We can generally anticipate when this will occur, and we can tell to what point of the heavens the telescope is to be pointed so as to discern the comet at its next return to perihelion. The comet cannot elude the grasp of the mathematician. He can tell when and where the comet is to be found, but no one can say what it will be like.