that the earth was the center of the universe; that the sun, the planets, and the countless stars revolved around and were accessory to this little abode of man.
Ptolemy, the greatest astronomer of the ancients, put this false theory on a strict mathematical basis. By means of his cumbersome system of epicycles he could roughly compute the positions of the planets at any time, could foretell the time of rising and setting of the moon, and predict eclipses. But, while the Ptolemaic system is false, while it does not agree with what we now know to be the true system of the heavens, yet it is mathematically possible. In discussing the various positions and motions of the planets, it would be perfectly possible to consider the earth as the fixed point around which they move; we could thus arrive at correct results, but the processes would be infinitely long and complicated. And yet a modification of this antiquated method was the only means of tracing further the path of this interesting comet, for the pull of Jupiter became now so strong that, in our backward path, we would have had to take steps, not of a few days, not of a few hours, but of twenty or thirty minutes at a time. The task would have been endless.
Jupiter was now the ruler of the comet's destiny, the sun a mere disturbing element, so that it became simpler to give Jupiter its just position as ruler at the center of the comet's motion.
Jupiter was made the momentary center of the universe; comet, sun, earth, and planets were all considered as revolving around this monster planet. The change of the center of motion from the sun to Jupiter was easily effected, and the resulting orbit of the comet about Jupiter was found to be a hyperbola, an open curve. And now, just as before, this curve is merely the path the comet would have described about Jupiter if it and the planet were the only two bodies in existence; the long-suffering comet is still pulled and hauled at by various bodies, notably the sun, and step by step its path had to be traced out. At first, steps of ten days each were found to be sufficiently accurate, but as the comet approached closer and closer to Jupiter it began to move faster and faster, and consequently the length of the steps had to be shortened to four days each. After the comet had passed Jupiter the length of the steps was gradually lengthened again.
The remarkable character of this appulse should be clearly understood. The comet passed the center of Jupiter in 1886, July 19th, at no greater distance than two and one third radii of that planet. It must then have passed the surface of Jupiter at a distance of only one and one third radii—that is, the center of the comet was only about sixty thousand miles from the surface of the planet. It is not at all improbable that parts of the diffused