No one had the slightest doubt but that this fantastical aurora borealis was the comet itself, a view confirmed by the fact that the former comet could not be found anywhere among the starry host. The apparition differed, it is true, from all popularly known cometary forms, and the radiating beams of the mysterious visitor were, of all forms, the least expected. But these gaseous bodies are so remarkable, so capricious, so various, that everything is possible. Moreover, it was not the first time that a comet had presented such an aspect. Astronomy contained among its records that of an immense comet observed in 1744, which at that time had been the subject of much discussion, and whose picturesque delineation, made de visu by the astronomer Chèzeaux, at Lausanne, had given it a wide celebrity. But even if nothing of this nature had been seen before, the evidence of one’s eyes was indubitable. Meanwhile, discussions multiplied, and a veritable astronomical tournament was commenced in the scientific reviews of the entire world—the only journals which inspired any confidence amid the epidemic of buying and selling which had for so long a time possessed humanity. The main question, now that there was no longer any doubt that the star was moving straight toward the earth, was its position from day to day, a question depending upon its velocity. The young computor of the Paris observatory, chief of the section of comets, sent every day a note to the official journal of the United States of Europe. [Illustration] A very simple mathematical relation exists between the velocity of every comet and its distance from the sun. Knowing the former one can at once find the latter. In fact the velocity of the comet is simply the velocity of a planet multiplied by the square root of two. Now the velocity of a planet, whatever its distance, is determined by Kepler’s third law, according to which the squares of the times of revolution are to each other as the cubes of the distances. Nothing evidently, can be more simple. Thus, for example, the magnificent planet, Jupiter, moves about the sun with a velocity of 13,000 meters per second. A comet at this distance moves, therefore, with the above-mentioned velocity, multiplied by the square root of two, that is to say by the number 1.4142. This velocity is consequently 18,380 meters per second. The planet Mars revolves about the sun at the rate of 24,000 meters per second. At this distance the comet’s velocity is 34,000 meters per second. The mean velocity of the earth in its orbit is 29,460 meters per second, a little less in June, a little more in December. In the neighborhood of the earth, therefore, the velocity of the comet is 41,660 meters, independently of the acceleration which the earth might occasion. These facts the laureate of the Institute called to the attention of the public which, moreover, already possessed some general notions upon the theory of celestial mechanics.